diff --git a/.github/CONTRIBUTING.md b/.github/CONTRIBUTING.md
index f3edd2bae51ab..cfb03d220c99c 100644
--- a/.github/CONTRIBUTING.md
+++ b/.github/CONTRIBUTING.md
@@ -130,11 +130,11 @@ In case you are adding new dependencies, make sure that they are compatible with
 
 ### Documentation
 
-To learn about development of docs, check out the docs [README.md](https://github.com/Lightning-AI/lightning/blob/master/docs/README.md).
+To learn about development of docs, check out the docs [README.md](https://github.com/Lightning-AI/pytorch-lightning/blob/master/docs/README.md).
 
 ### Testing
 
-To learn about tests, check out the tests [README.md](https://github.com/Lightning-AI/lightning/blob/master/tests/README.md).
+To learn about tests, check out the tests [README.md](https://github.com/Lightning-AI/pytorch-lightning/blob/master/tests/README.md).
 
 ### Pull Request
 
@@ -165,8 +165,8 @@ We welcome any useful contribution! For your convenience here's a recommended wo
 
 1. If any of the existing tests fail in your PR on our CI, refer to the following READMEs to identify what's failing and try to address it.
 
-   - [Test README](https://github.com/Lightning-AI/lightning/blob/master/tests/README.md)
-   - [CI/CD README](https://github.com/Lightning-AI/lightning/blob/master/.github/workflows/README.md)
+   - [Test README](https://github.com/Lightning-AI/pytorch-lightning/blob/master/tests/README.md)
+   - [CI/CD README](https://github.com/Lightning-AI/pytorch-lightning/tree/master/.github/workflows#readme)
 
 1. When you feel ready for integrating your work, mark your PR "Ready for review".
 
diff --git a/.github/PULL_REQUEST_TEMPLATE.md b/.github/PULL_REQUEST_TEMPLATE.md
index fe89375a04e83..cd784a5037525 100644
--- a/.github/PULL_REQUEST_TEMPLATE.md
+++ b/.github/PULL_REQUEST_TEMPLATE.md
@@ -18,7 +18,7 @@ Fixes #\<issue_number>
   <summary><b>Before submitting</b></summary>
 
 - Was this **discussed/agreed** via a GitHub issue? (not for typos and docs)
-- [ ] Did you read the [contributor guideline](https://github.com/Lightning-AI/lightning/blob/master/.github/CONTRIBUTING.md), **Pull Request** section?
+- [ ] Did you read the [contributor guideline](https://github.com/Lightning-AI/pytorch-lightning/blob/master/.github/CONTRIBUTING.md), **Pull Request** section?
 - [ ] Did you make sure your **PR does only one thing**, instead of bundling different changes together?
 - Did you make sure to **update the documentation** with your changes? (if necessary)
 - Did you write any **new necessary tests**? (not for typos and docs)
diff --git a/.github/markdown-links-config.json b/.github/markdown-links-config.json
index 1447e5c8ea832..bc9721da2c587 100644
--- a/.github/markdown-links-config.json
+++ b/.github/markdown-links-config.json
@@ -2,6 +2,12 @@
   "ignorePatterns": [
     {
       "pattern": "^https://github.com/Lightning-AI/pytorch-lightning/pull/"
+    },
+    {
+      "pattern": "^https://dev.azure.com/Lightning-AI/lightning/_apis/build/status"
+    },
+    {
+      "pattern": "^https://codecov.io/gh/Lightning-AI/pytorch-lightning/graph/badge.svg"
     }
   ],
   "httpHeaders": [
diff --git a/.github/workflows/ci-check-md-links.yml b/.github/workflows/ci-check-md-links.yml
index efae72a87f86c..12aca9547e7c7 100644
--- a/.github/workflows/ci-check-md-links.yml
+++ b/.github/workflows/ci-check-md-links.yml
@@ -9,12 +9,13 @@ on:
     types: [opened, reopened, ready_for_review, synchronize]
     paths:
       - ".github/workflows/ci-check-md-links.yml"
-      - ".github/workflows/markdown.links.config.json"
+      - ".github/markdown-links-config.json"
       - "**/*.md"
 
 jobs:
   check-md-links:
-    uses: Lightning-AI/utilities/.github/workflows/check-md-links.yml@v0.14.3
+    uses: Lightning-AI/utilities/.github/workflows/check-md-links.yml@main # can be pin with >=0.14.4
     with:
       config-file: ".github/markdown-links-config.json"
       base-branch: "master"
+      force-check-all: "yes"
diff --git a/README.md b/README.md
index aa58c6d8a585a..dd5f0fe43e0c7 100644
--- a/README.md
+++ b/README.md
@@ -31,7 +31,7 @@ ______________________________________________________________________
 
 [![Discord](https://img.shields.io/discord/1077906959069626439?style=plastic)](https://discord.gg/VptPCZkGNa)
 ![GitHub commit activity](https://img.shields.io/github/commit-activity/w/lightning-ai/lightning)
-[![license](https://img.shields.io/badge/License-Apache%202.0-blue.svg)](https://github.com/Lightning-AI/lightning/blob/master/LICENSE)
+[![license](https://img.shields.io/badge/License-Apache%202.0-blue.svg)](https://github.com/Lightning-AI/pytorch-lightning/blob/master/LICENSE)
 
 <!--
 [![CodeFactor](https://www.codefactor.io/repository/github/Lightning-AI/lightning/badge)](https://www.codefactor.io/repository/github/Lightning-AI/lightning)
diff --git a/docs/source-fabric/_templates/theme_variables.jinja b/docs/source-fabric/_templates/theme_variables.jinja
index e2ebb66281716..d379400c01d84 100644
--- a/docs/source-fabric/_templates/theme_variables.jinja
+++ b/docs/source-fabric/_templates/theme_variables.jinja
@@ -1,7 +1,7 @@
 {%- set external_urls = {
   'github': 'https://github.com/Lightning-AI/lightning',
   'github_issues': 'https://github.com/Lightning-AI/pytorch-lightning/issues',
-  'contributing': 'https://github.com/Lightning-AI/lightning/blob/master/.github/CONTRIBUTING.md',
+  'contributing': 'https://github.com/Lightning-AI/pytorch-lightning/blob/master/.github/CONTRIBUTING.md',
   'governance': 'https://lightning.ai/docs/pytorch/latest/community/governance.html',
   'docs': 'https://lightning.ai/docs/fabric/',
   'twitter': 'https://twitter.com/LightningAI',
diff --git a/docs/source-fabric/advanced/compile.rst b/docs/source-fabric/advanced/compile.rst
index df79454f67a6f..cc8fe39c683d4 100644
--- a/docs/source-fabric/advanced/compile.rst
+++ b/docs/source-fabric/advanced/compile.rst
@@ -221,7 +221,7 @@ needed to achieve the equivalent of `compile(distributed(quantized(model)))`:
 
         model = fabric.setup(model)
 
-For a full example, see our `FP8 Distributed Transformer example <https://github.com/Lightning-AI/lightning/blob/master/examples/fabric/fp8_distributed_transformer>`_.
+For a full example, see our `FP8 Distributed Transformer example <https://github.com/Lightning-AI/pytorch-lightning/blob/master/examples/fabric/fp8_distributed_transformer>`_.
 
 ----
 
diff --git a/docs/source-fabric/advanced/multiple_setup.rst b/docs/source-fabric/advanced/multiple_setup.rst
index 1ecdcc9dee79b..27c1dfbe9c105 100644
--- a/docs/source-fabric/advanced/multiple_setup.rst
+++ b/docs/source-fabric/advanced/multiple_setup.rst
@@ -113,4 +113,4 @@ You can pair up as many models and optimizers as you want. For example, two mode
     # Set up discriminator
     discriminator, optimizer_dis = fabric.setup(discriminator, optimizer_dis)
 
-For a full example of this use case, see our `GAN example <https://github.com/Lightning-AI/lightning/blob/master/examples/fabric/dcgan>`_.
+For a full example of this use case, see our `GAN example <https://github.com/Lightning-AI/pytorch-lightning/blob/master/examples/fabric/dcgan>`_.
diff --git a/docs/source-fabric/examples/index.rst b/docs/source-fabric/examples/index.rst
index f5478fb48f882..563c2b1e043b2 100644
--- a/docs/source-fabric/examples/index.rst
+++ b/docs/source-fabric/examples/index.rst
@@ -10,7 +10,7 @@ Examples
 .. displayitem::
     :header: Image Classification
     :description: Train an image classifier on the MNIST dataset
-    :button_link: https://github.com/Lightning-AI/lightning/blob/master/examples/fabric/image_classifier
+    :button_link: https://github.com/Lightning-AI/pytorch-lightning/blob/master/examples/fabric/image_classifier
     :col_css: col-md-4
     :height: 200
     :tag: basic
@@ -18,7 +18,7 @@ Examples
 .. displayitem::
     :header: Transformer Language Model
     :description: A simple language model that learns to predict the next word in a sentence
-    :button_link: https://github.com/Lightning-AI/lightning/blob/master/examples/fabric/language_model
+    :button_link: https://github.com/Lightning-AI/pytorch-lightning/blob/master/examples/fabric/language_model
     :col_css: col-md-4
     :height: 200
     :tag: basic
@@ -26,7 +26,7 @@ Examples
 .. displayitem::
     :header: GAN
     :description: Train a GAN that generates realistic human faces
-    :button_link: https://github.com/Lightning-AI/lightning/blob/master/examples/fabric/dcgan
+    :button_link: https://github.com/Lightning-AI/pytorch-lightning/blob/master/examples/fabric/dcgan
     :col_css: col-md-4
     :height: 200
     :tag: intermediate
@@ -34,7 +34,7 @@ Examples
 .. displayitem::
     :header: Meta-Learning
     :description: Distributed training with the MAML algorithm on the Omniglot and MiniImagenet datasets
-    :button_link: https://github.com/Lightning-AI/lightning/blob/master/examples/fabric/meta_learning
+    :button_link: https://github.com/Lightning-AI/pytorch-lightning/blob/master/examples/fabric/meta_learning
     :col_css: col-md-4
     :height: 200
     :tag: intermediate
@@ -50,7 +50,7 @@ Examples
 .. displayitem::
     :header: Reinforcement Learning
     :description: Implementation of the Proximal Policy Optimization (PPO) algorithm with multi-GPU support
-    :button_link: https://github.com/Lightning-AI/lightning/blob/master/examples/fabric/reinforcement_learning
+    :button_link: https://github.com/Lightning-AI/pytorch-lightning/blob/master/examples/fabric/reinforcement_learning
     :col_css: col-md-4
     :height: 200
     :tag: intermediate
diff --git a/docs/source-fabric/fundamentals/convert.rst b/docs/source-fabric/fundamentals/convert.rst
index 6f1a175eef8bc..e4f497ae075b6 100644
--- a/docs/source-fabric/fundamentals/convert.rst
+++ b/docs/source-fabric/fundamentals/convert.rst
@@ -84,7 +84,7 @@ All steps combined, this is how your code will change:
 
 
 That's it! You can now train on any device at any scale with a switch of a flag.
-Check out our before-and-after example for `image classification <https://github.com/Lightning-AI/lightning/blob/master/examples/fabric/image_classifier/README.md>`_ and many more :doc:`examples <../examples/index>` that use Fabric.
+Check out our before-and-after example for `image classification <https://github.com/Lightning-AI/pytorch-lightning/blob/master/examples/fabric/image_classifier/README.md>`_ and many more :doc:`examples <../examples/index>` that use Fabric.
 
 
 ----
diff --git a/docs/source-pytorch/_templates/theme_variables.jinja b/docs/source-pytorch/_templates/theme_variables.jinja
index 3e6a4d19bdeed..f514f7f06fd01 100644
--- a/docs/source-pytorch/_templates/theme_variables.jinja
+++ b/docs/source-pytorch/_templates/theme_variables.jinja
@@ -1,7 +1,7 @@
 {%- set external_urls = {
   'github': 'https://github.com/Lightning-AI/lightning',
   'github_issues': 'https://github.com/Lightning-AI/pytorch-lightning/issues',
-  'contributing': 'https://github.com/Lightning-AI/lightning/blob/master/.github/CONTRIBUTING.md',
+  'contributing': 'https://github.com/Lightning-AI/pytorch-lightning/blob/master/.github/CONTRIBUTING.md',
   'governance': 'https://lightning.ai/docs/pytorch/latest/community/governance.html',
   'docs': 'https://lightning.ai/docs/pytorch/latest/',
   'twitter': 'https://twitter.com/LightningAI',
diff --git a/docs/source-pytorch/advanced/compile.rst b/docs/source-pytorch/advanced/compile.rst
index 90a5a1f508189..dba611c79a475 100644
--- a/docs/source-pytorch/advanced/compile.rst
+++ b/docs/source-pytorch/advanced/compile.rst
@@ -251,7 +251,7 @@ needed to achieve the equivalent of `compile(distributed(quantized(model)))`:
 
             self.model = torch.compile(model)
 
-For a full example, see our `FP8 Distributed Transformer example <https://github.com/Lightning-AI/lightning/blob/master/examples/pytorch/fp8_distributed_transformer>`_.
+For a full example, see our `FP8 Distributed Transformer example <https://github.com/Lightning-AI/pytorch-lightning/blob/master/examples/pytorch/fp8_distributed_transformer>`_.
 
 ----
 
diff --git a/docs/source-pytorch/community/governance.rst b/docs/source-pytorch/community/governance.rst
index 58a731d0576e3..b4345a33f3626 100644
--- a/docs/source-pytorch/community/governance.rst
+++ b/docs/source-pytorch/community/governance.rst
@@ -67,6 +67,6 @@ and start tracking the development. It is possible that priorities change over t
 
 Commits to the project are exclusively to be added by pull requests on GitHub and anyone in the community is welcome to
 review them. However, reviews submitted by
-`code owners <https://github.com/Lightning-AI/lightning/blob/master/.github/CODEOWNERS>`_
+`code owners <https://github.com/Lightning-AI/pytorch-lightning/blob/master/.github/CODEOWNERS>`_
 have higher weight and it is necessary to get the approval of code owners before a pull request can be merged.
 Additional requirements may apply case by case.
diff --git a/examples/fabric/meta_learning/README.md b/examples/fabric/meta_learning/README.md
index 31a87932007f8..c9329aacf49fc 100644
--- a/examples/fabric/meta_learning/README.md
+++ b/examples/fabric/meta_learning/README.md
@@ -1,7 +1,7 @@
 ## Meta-Learning - MAML
 
 This is an example of a meta-learning algorithm called [MAML](https://arxiv.org/abs/1703.03400), trained on the
-[Omniglot dataset](https://paperswithcode.com/dataset/omniglot-1) of handwritten characters from different alphabets.
+[Omniglot dataset](https://github.com/brendenlake/omniglot) of handwritten characters from different alphabets.
 
 The goal of meta-learning in this context is to learn a 'meta'-model trained on many different tasks, such that it can quickly adapt to a new task when trained with very few samples (few-shot learning).
 If you are new to meta-learning, have a look at this short [introduction video](https://www.youtube.com/watch?v=ItPEBdD6VMk).
diff --git a/src/lightning/data/README.md b/src/lightning/data/README.md
index c61e7eacf26f2..94c5f616df600 100644
--- a/src/lightning/data/README.md
+++ b/src/lightning/data/README.md
@@ -15,7 +15,7 @@ We developed `StreamingDataset` to optimize training of large datasets stored on
 
 Specifically crafted for multi-gpu & multi-node (with [DDP](https://lightning.ai/docs/pytorch/stable/accelerators/gpu_intermediate.html), [FSDP](https://lightning.ai/docs/pytorch/stable/advanced/model_parallel/fsdp.html), etc...), distributed training with large models, it enhances accuracy, performance, and user-friendliness. Now, training efficiently is possible regardless of the data's location. Simply stream in the required data when needed.
 
-The `StreamingDataset` is compatible with any data type, including **images, text, video, audio, geo-spatial, and multimodal data** and it is a drop-in replacement for your PyTorch [IterableDataset](https://pytorch.org/docs/stable/data.html#torch.utils.data.IterableDataset) class. For example, it is used by [Lit-GPT](https://github.com/Lightning-AI/lit-gpt/blob/main/litgpt/data/tinyllama.py) to pretrain LLMs.
+The `StreamingDataset` is compatible with any data type, including **images, text, video, audio, geo-spatial, and multimodal data** and it is a drop-in replacement for your PyTorch [IterableDataset](https://pytorch.org/docs/stable/data.html#torch.utils.data.IterableDataset) class. For example, it is used by [Lit-GPT](https://github.com/Lightning-AI/litgpt/blob/main/litgpt/data/tinyllama.py) to pretrain LLMs.
 
 <br/>
 
@@ -284,7 +284,7 @@ for batch in tqdm(train_dataloader):
 
 Lightning Data provides a stateful `StreamingDataLoader`. This simplifies resuming training over large datasets.
 
-Note: The `StreamingDataLoader` is used by [Lit-GPT](https://github.com/Lightning-AI/lit-gpt/blob/main/litgpt/data/tinyllama.py) to pretrain LLMs. The statefulness still works when using a mixture of datasets with the `CombinedStreamingDataset`.
+Note: The `StreamingDataLoader` is used by [Lit-GPT](https://github.com/Lightning-AI/litgpt/blob/main/litgpt/data/tinyllama.py) to pretrain LLMs. The statefulness still works when using a mixture of datasets with the `CombinedStreamingDataset`.
 
 ```python
 import os
diff --git a/src/pytorch_lightning/README.md b/src/pytorch_lightning/README.md
index f3fb8cb2fd2b3..e3878c501967f 100644
--- a/src/pytorch_lightning/README.md
+++ b/src/pytorch_lightning/README.md
@@ -15,7 +15,7 @@ ______________________________________________________________________
   <a href="#examples">Examples</a> •
   <a href="#community">Community</a> •
   <a href="https://lightning.ai/">Lightning AI</a> •
-  <a href="https://github.com/Lightning-AI/lightning/blob/master/LICENSE">License</a>
+  <a href="https://github.com/Lightning-AI/pytorch-lightning/blob/master/LICENSE">License</a>
 </p>
 
 <!-- DO NOT ADD CONDA DOWNLOADS... README CHANGES MUST BE APPROVED BY EDEN OR WILL -->
@@ -28,7 +28,7 @@ ______________________________________________________________________
 [![codecov](https://codecov.io/gh/Lightning-AI/pytorch-lightning/graph/badge.svg?token=SmzX8mnKlA)](https://codecov.io/gh/Lightning-AI/pytorch-lightning)
 
 [![ReadTheDocs](https://readthedocs.org/projects/pytorch-lightning/badge/?version=stable)](https://lightning.ai/docs/pytorch/stable/)[![Discord](https://img.shields.io/discord/1077906959069626439?style=plastic)](https://discord.gg/VptPCZkGNa)
-[![license](https://img.shields.io/badge/License-Apache%202.0-blue.svg)](https://github.com/Lightning-AI/lightning/blob/master/LICENSE)
+[![license](https://img.shields.io/badge/License-Apache%202.0-blue.svg)](https://github.com/Lightning-AI/pytorch-lightning/blob/master/LICENSE)
 
 <!--
 [![CodeFactor](https://www.codefactor.io/repository/github/Lightning-AI/lightning/badge)](https://www.codefactor.io/repository/github/Lightning-AI/lightning)
diff --git a/tests/README.md b/tests/README.md
index 9265caf4b412e..26e49c4f5751f 100644
--- a/tests/README.md
+++ b/tests/README.md
@@ -1,6 +1,6 @@
 # PyTorch-Lightning Tests
 
-Most of the tests in PyTorch Lightning train a [BoringModel](https://github.com/Lightning-AI/lightning/blob/master/src/lightning/pytorch/demos/boring_classes.py) under various trainer conditions (ddp, amp, etc...). Want to add a new test case and not sure how? [Talk to us!](https://www.pytorchlightning.ai/community)
+Most of the tests in PyTorch Lightning train a [BoringModel](https://github.com/Lightning-AI/pytorch-lightning/blob/master/src/lightning/pytorch/demos/boring_classes.py) under various trainer conditions (ddp, amp, etc...). Want to add a new test case and not sure how? [Talk to us!](https://www.pytorchlightning.ai/community)
 
 ## Running tests
 
@@ -26,7 +26,7 @@ Additionally, for testing backward compatibility with older versions of PyTorch
 bash .actions/pull_legacy_checkpoints.sh
 ```
 
-Note: These checkpoints are generated to set baselines for maintaining backward compatibility with legacy versions of PyTorch Lightning. Details of checkpoints for back-compatibility can be found [here](https://github.com/Lightning-AI/lightning/blob/master/tests/legacy/README.md).
+Note: These checkpoints are generated to set baselines for maintaining backward compatibility with legacy versions of PyTorch Lightning. Details of checkpoints for back-compatibility can be found [here](https://github.com/Lightning-AI/pytorch-lightning/blob/master/tests/legacy/README.md).
 
 You can run the full test suite in your terminal via this make script: