diff --git a/Project.toml b/Project.toml
index e5befc8145..d881749ba7 100644
--- a/Project.toml
+++ b/Project.toml
@@ -3,5 +3,11 @@ uuid = "9136182c-28ba-11e9-034c-db9fb085ebd5"
 authors = ["ITensor developers <support@itensor.org> and contributors"]
 version = "0.8.0"
 
+[deps]
+BroadcastMapConversion = "4a4adec5-520f-4750-bb37-d5e66b4ddeb2"
+NamedDimsArrays = "60cbd0c0-df58-4cb7-918c-6f5607b73fde"
+
 [compat]
+BroadcastMapConversion = "0.1.2"
+NamedDimsArrays = "0.3.0"
 julia = "1.10"
diff --git a/README.md b/README.md
index f3db44263e..81c3269b8f 100644
--- a/README.md
+++ b/README.md
@@ -9,21 +9,7 @@
 
 ## Installation instructions
 
-This package resides in the `ITensor/ITensorRegistry` local registry.
-In order to install, simply add that registry through your package manager.
-This step is only required once.
-```julia
-julia> using Pkg: Pkg
-
-julia> Pkg.Registry.add(url="https://github.com/ITensor/ITensorRegistry")
-```
-or:
-```julia
-julia> Pkg.Registry.add(url="git@github.com:ITensor/ITensorRegistry.git")
-```
-if you want to use SSH credentials, which can make it so you don't have to enter your Github ursername and password when registering packages.
-
-Then, the package can be added as usual through the package manager:
+The package can be added as usual through the package manager:
 
 ```julia
 julia> Pkg.add("ITensors")
@@ -32,10 +18,31 @@ julia> Pkg.add("ITensors")
 ## Examples
 
 ````julia
-using ITensors: ITensors
+using ITensors: ITensors, ITensor, Index
 ````
 
-Examples go here.
+TODO: This should be `TensorAlgebra.qr`.
+
+````julia
+using LinearAlgebra: qr
+using NamedDimsArrays: NamedDimsArray, aligndims, dimnames, name, unname
+using Test: @test
+i = Index(2)
+j = Index(2)
+k = Index(2)
+a = randn(i, j)
+@test a[j[2], i[1]] == a[1, 2]
+@test a[j => 2, i => 1] == a[1, 2]
+a′ = randn(j, i)
+b = randn(j, k)
+c = a * b
+@test unname(c, (i, k)) ≈ unname(a, (i, j)) * unname(b, (j, k))
+d = a + a′
+@test unname(d, (i, j)) ≈ unname(a, (i, j)) + unname(a′, (i, j))
+@test a ≈ aligndims(a, (j, i))
+q, r = qr(a, (i,))
+@test q * r ≈ a
+````
 
 ---
 
diff --git a/TODO.md b/TODO.md
new file mode 100644
index 0000000000..dbeebed684
--- /dev/null
+++ b/TODO.md
@@ -0,0 +1,54 @@
+- Logic around element type promotion, BangBang.jl syntax.
+```julia
+module MutableStorageArrays
+
+module NoBang
+function setindex(a::AbstractArray, value, I::Int...)
+  a′ = similar(a, typeof(value))
+  a′ .= a
+  a′[I...] = value
+  return a′
+end
+
+function setindex(a::AbstractArray, value, I...)
+  a′ = similar(a, eltype(value))
+  a′ .= a
+  a′[I...] = value
+  return a′
+end
+end
+
+function may(f!, args...)
+  if possible(f!, args...)
+    return f!(args...)
+  end
+  return pure(f!)(args...)
+end
+
+implements(f!, x) = implements(f!, typeof(x))
+implements(f!, ::Type) = false
+
+function setindex!! end
+setindex!!(a::AbstractArray, value, I...) = may(setindex!, a, value, I...)
+implements(::typeof(setindex!), ::Type{<:AbstractArray}) = true
+pure(::typeof(setindex!)) = NoBang.setindex
+maymutate(::typeof(setindex!)) = setindex!!
+function possible(::typeof(setindex!), a::AbstractArray, value, I::Int...)
+  return implements(setindex!, a) && promote_type(eltype(a), typeof(value)) <: eltype(a)
+end
+function possible(::typeof(setindex!), a::AbstractArray, value, I...)
+  return implements(setindex!, a) && promote_type(eltype(a), eltype(value)) <: eltype(a)
+end
+
+struct MutableStorageArrayInterface <: AbstractArrayInterface end
+
+# Minimal interface.
+function storage end
+function setstorage! end
+
+@interface ::MutableStorageArrayInterface function Base.setindex!(a::AbstractArray, value, I...)
+  return setstorage!(a, storage(setindex!!(a, value, I...)))
+end
+
+end
+```
diff --git a/docs/Project.toml b/docs/Project.toml
index d0900102a4..0a8148e75f 100644
--- a/docs/Project.toml
+++ b/docs/Project.toml
@@ -1,4 +1,5 @@
 [deps]
-ITensors = "3b3c2350-9fb7-4c22-a0c2-b3f20f86ea25"
 Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4"
+ITensors = "9136182c-28ba-11e9-034c-db9fb085ebd5"
 Literate = "98b081ad-f1c9-55d3-8b20-4c87d4299306"
+NamedDimsArrays = "60cbd0c0-df58-4cb7-918c-6f5607b73fde"
diff --git a/examples/Project.toml b/examples/Project.toml
index e8bc93e8a6..2d73659e0d 100644
--- a/examples/Project.toml
+++ b/examples/Project.toml
@@ -1,2 +1,4 @@
 [deps]
-ITensors = "3b3c2350-9fb7-4c22-a0c2-b3f20f86ea25"
+ITensors = "9136182c-28ba-11e9-034c-db9fb085ebd5"
+LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
+NamedDimsArrays = "60cbd0c0-df58-4cb7-918c-6f5607b73fde"
diff --git a/examples/README.jl b/examples/README.jl
index 00d68cfe9d..5ece9c9ba5 100644
--- a/examples/README.jl
+++ b/examples/README.jl
@@ -9,25 +9,7 @@
 
 # ## Installation instructions
 
-# This package resides in the `ITensor/ITensorRegistry` local registry.
-# In order to install, simply add that registry through your package manager.
-# This step is only required once.
-#=
-```julia
-julia> using Pkg: Pkg
-
-julia> Pkg.Registry.add(url="https://github.com/ITensor/ITensorRegistry")
-```
-=#
-# or:
-#=
-```julia
-julia> Pkg.Registry.add(url="git@github.com:ITensor/ITensorRegistry.git")
-```
-=#
-# if you want to use SSH credentials, which can make it so you don't have to enter your Github ursername and password when registering packages.
-
-# Then, the package can be added as usual through the package manager:
+# The package can be added as usual through the package manager:
 
 #=
 ```julia
@@ -37,5 +19,23 @@ julia> Pkg.add("ITensors")
 
 # ## Examples
 
-using ITensors: ITensors
-# Examples go here.
+using ITensors: ITensors, ITensor, Index
+# TODO: This should be `TensorAlgebra.qr`.
+using LinearAlgebra: qr
+using NamedDimsArrays: NamedDimsArray, aligndims, dimnames, name, unname
+using Test: @test
+i = Index(2)
+j = Index(2)
+k = Index(2)
+a = randn(i, j)
+@test a[j[2], i[1]] == a[1, 2]
+@test a[j => 2, i => 1] == a[1, 2]
+a′ = randn(j, i)
+b = randn(j, k)
+c = a * b
+@test unname(c, (i, k)) ≈ unname(a, (i, j)) * unname(b, (j, k))
+d = a + a′
+@test unname(d, (i, j)) ≈ unname(a, (i, j)) + unname(a′, (i, j))
+@test a ≈ aligndims(a, (j, i))
+q, r = qr(a, (i,))
+@test q * r ≈ a
diff --git a/src/ITensors.jl b/src/ITensors.jl
index ce4be0e50f..222c546a8b 100644
--- a/src/ITensors.jl
+++ b/src/ITensors.jl
@@ -1,5 +1,79 @@
 module ITensors
 
-# Write your package code here.
+using BroadcastMapConversion: Mapped
+using NamedDimsArrays:
+  NamedDimsArrays,
+  AbstractName,
+  AbstractNamedDimsArray,
+  AbstractNamedInteger,
+  AbstractNamedUnitRange,
+  AbstractNamedVector,
+  dename,
+  dimnames,
+  name,
+  named,
+  unname
+
+@kwdef struct IndexName <: AbstractName
+  id::UInt64 = rand(UInt64)
+  plev::Int = 0
+  tags::Set{String} = Set{String}()
+  namedtags::Dict{Symbol,String} = Dict{Symbol,String}()
+end
+NamedDimsArrays.randname(n::IndexName) = IndexName()
+
+struct IndexVal{Value<:Integer} <: AbstractNamedInteger{Value,IndexName}
+  value::Value
+  name::IndexName
+end
+
+# Interface
+NamedDimsArrays.dename(i::IndexVal) = i.value
+NamedDimsArrays.name(i::IndexVal) = i.name
+
+# Constructor
+NamedDimsArrays.named(i::Integer, name::IndexName) = IndexVal(i, name)
+
+struct Index{T,Value<:AbstractUnitRange{T}} <: AbstractNamedUnitRange{T,Value,IndexName}
+  value::Value
+  name::IndexName
+end
+
+Index(length::Int) = Index(Base.OneTo(length), IndexName())
+
+# Interface
+# TODO: Overload `Base.parent` instead.
+NamedDimsArrays.dename(i::Index) = i.value
+NamedDimsArrays.name(i::Index) = i.name
+
+# Constructor
+NamedDimsArrays.named(i::AbstractUnitRange, name::IndexName) = Index(i, name)
+
+struct NoncontiguousIndex{T,Value<:AbstractVector{T}} <:
+       AbstractNamedVector{T,Value,IndexName}
+  value::Value
+  name::IndexName
+end
+
+# Interface
+# TODO: Overload `Base.parent` instead.
+NamedDimsArrays.dename(i::NoncontiguousIndex) = i.value
+NamedDimsArrays.name(i::NoncontiguousIndex) = i.name
+
+# Constructor
+NamedDimsArrays.named(i::AbstractVector, name::IndexName) = NoncontiguousIndex(i, name)
+
+abstract type AbstractITensor <: AbstractNamedDimsArray{Any,Any} end
+
+NamedDimsArrays.nameddimsarraytype(::Type{<:IndexName}) = ITensor
+
+Base.ndims(::Type{<:AbstractITensor}) = Any
+
+struct ITensor <: AbstractITensor
+  parent::AbstractArray
+  nameddimsindices
+end
+Base.parent(a::ITensor) = a.parent
+NamedDimsArrays.nameddimsindices(a::ITensor) = a.nameddimsindices
 
 end
diff --git a/test/Project.toml b/test/Project.toml
index e9c291ea3a..6d76ee2d69 100644
--- a/test/Project.toml
+++ b/test/Project.toml
@@ -1,5 +1,8 @@
 [deps]
 Aqua = "4c88cf16-eb10-579e-8560-4a9242c79595"
+ITensors = "9136182c-28ba-11e9-034c-db9fb085ebd5"
+LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
+NamedDimsArrays = "60cbd0c0-df58-4cb7-918c-6f5607b73fde"
 SafeTestsets = "1bc83da4-3b8d-516f-aca4-4fe02f6d838f"
 Suppressor = "fd094767-a336-5f1f-9728-57cf17d0bbfb"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"