diff --git a/ChangeLog.md b/ChangeLog.md
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+++ b/ChangeLog.md
@@ -0,0 +1,6 @@
+# Changelog for composite-ix
+
+## 0.0.1.0
+
+* Added module `Composite.Ix.Vector`.
+* Added modules `Composite.Ix.List` and `Composite.Ix.NonEmpty`.
diff --git a/LICENSE b/LICENSE
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--- /dev/null
+++ b/LICENSE
@@ -0,0 +1,30 @@
+Copyright Author name here (c) 2022
+
+All rights reserved.
+
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions are met:
+
+    * Redistributions of source code must retain the above copyright
+      notice, this list of conditions and the following disclaimer.
+
+    * Redistributions in binary form must reproduce the above
+      copyright notice, this list of conditions and the following
+      disclaimer in the documentation and/or other materials provided
+      with the distribution.
+
+    * Neither the name of Author name here nor the names of other
+      contributors may be used to endorse or promote products derived
+      from this software without specific prior written permission.
+
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
+OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
+LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
diff --git a/README.md b/README.md
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--- /dev/null
+++ b/README.md
@@ -0,0 +1,1 @@
+# composite-ix
diff --git a/composite-ix.cabal b/composite-ix.cabal
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--- /dev/null
+++ b/composite-ix.cabal
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+cabal-version: 1.12
+
+-- This file has been generated from package.yaml by hpack version 0.34.6.
+--
+-- see: https://github.com/sol/hpack
+
+name:           composite-ix
+version:        0.0.1.0
+synopsis:       Indexing utilities for composite records.
+description:    Indexing utilities for composite records.
+category:       Web
+author:         Daniel Firth
+maintainer:     dan.firth@homotopic.tech
+copyright:      2022 Daniel Firth
+license:        BSD3
+license-file:   LICENSE
+build-type:     Simple
+extra-source-files:
+    README.md
+    ChangeLog.md
+
+source-repository head
+  type: git
+  location: https://gitlab.homotopic.tech/haskell/composite-ix
+
+library
+  exposed-modules:
+      Composite.Ix.List
+      Composite.Ix.NonEmpty
+      Composite.Ix.Vector
+  other-modules:
+      Paths_composite_ix
+  hs-source-dirs:
+      src
+  default-extensions:
+      AllowAmbiguousTypes
+      DeriveGeneric
+      DerivingStrategies
+      FlexibleContexts
+      GADTs
+      RankNTypes
+      ScopedTypeVariables
+      StandaloneDeriving
+      TypeApplications
+      TypeOperators
+  build-depends:
+      base >=4.7 && <5
+    , composite-base
+    , containers
+    , lens
+    , nonempty-containers
+    , vector
+    , vinyl
+  default-language: Haskell2010
diff --git a/src/Composite/Ix/List.hs b/src/Composite/Ix/List.hs
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--- /dev/null
+++ b/src/Composite/Ix/List.hs
@@ -0,0 +1,41 @@
+module Composite.Ix.List (groupBy, groupBy', groupBy'') where
+
+import           Composite.Record
+import           Control.Lens
+import qualified Data.Map         as M
+import           Data.Proxy
+import           Data.Vinyl       hiding (rlens, rlens')
+import           Prelude
+
+-- | Group a list of records by a subtype of the record type.
+--
+-- @since 0.0.1.0
+groupBy :: forall ys xs f.
+           (ys ⊆ xs)
+        => Ord (Rec f ys)
+        => [Rec f xs]
+        -> M.Map (Rec f ys) [Rec f xs]
+groupBy xs = M.fromListWith (<>) $ fmap (\x -> (rcast x, [x])) xs
+
+-- | Group a list of records by a single field.
+--
+-- @since 0.0.1.0
+groupBy' :: forall k s y xs.
+            k ~ (s :-> y)
+         => k ∈ xs
+         => Ord y
+         => [Record xs]
+         -> M.Map y [Record xs]
+groupBy' xs = M.fromListWith (<>) $ fmap (\x -> (view (rlens (Proxy @(s :-> y))) x, [x])) xs
+
+-- | Group a list of records by a single field (HKD).
+--
+-- @since 0.0.1.0
+groupBy'' :: forall k s y xs f.
+             k ~ (s :-> y)
+          => k ∈ xs
+          => Functor f
+          => Ord (f y)
+          => [Rec f xs]
+          -> M.Map (f y) [Rec f xs]
+groupBy'' xs = M.fromListWith (<>) $ fmap (\x -> (view (rlens' (Proxy @(s :-> y))) x, [x])) xs
diff --git a/src/Composite/Ix/NonEmpty.hs b/src/Composite/Ix/NonEmpty.hs
new file mode 100644
--- /dev/null
+++ b/src/Composite/Ix/NonEmpty.hs
@@ -0,0 +1,42 @@
+module Composite.Ix.NonEmpty (groupBy, groupBy', groupBy'') where
+
+import           Composite.Record
+import           Control.Lens
+import           Data.List.NonEmpty (NonEmpty ((:|)))
+import qualified Data.List.NonEmpty as NE
+import qualified Data.Map.NonEmpty  as MNE
+import           Data.Proxy
+import           Data.Vinyl         hiding (rlens, rlens')
+
+-- | Group a NonEmpty list of records by a subtype of the record.
+--
+-- @since 0.0.1.0
+groupBy :: forall ys xs f.
+           (ys ⊆ xs)
+        => Ord (Rec f ys)
+        => NonEmpty (Rec f xs)
+        -> MNE.NEMap (Rec f ys) (NonEmpty (Rec f xs))
+groupBy xs = MNE.fromListWith (<>) $ fmap (\x -> (rcast x, x :| [])) xs
+
+-- | Group a NonEmpty list of records by a single field.
+--
+-- @since 0.0.1.0
+groupBy' :: forall k s y xs.
+            k ~ (s :-> y)
+         => k ∈ xs
+         => Ord y
+         => NonEmpty (Record xs)
+         -> MNE.NEMap y (NonEmpty (Record xs))
+groupBy' xs = MNE.fromListWith (<>) $ fmap (\x -> (view (rlens (Proxy @(s :-> y))) x, x :| [])) xs
+
+-- | Group a NonEmpty list of records by a single field (HKD).
+--
+-- @since 0.0.1.0
+groupBy'' :: forall k s y xs f.
+             k ~ (s :-> y)
+          => k ∈ xs
+          => Functor f
+          => Ord (f y)
+          => NonEmpty (Rec f xs)
+          -> MNE.NEMap (f y) (NonEmpty (Rec f xs))
+groupBy'' xs = MNE.fromListWith (<>) $ fmap (\x -> (view (rlens' (Proxy @(s :-> y))) x, x :| [])) xs
diff --git a/src/Composite/Ix/Vector.hs b/src/Composite/Ix/Vector.hs
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--- /dev/null
+++ b/src/Composite/Ix/Vector.hs
@@ -0,0 +1,42 @@
+module Composite.Ix.Vector (groupBy, groupBy', groupBy'') where
+
+import           Composite.Record
+import           Control.Lens
+import qualified Data.Map         as M
+import           Data.Proxy
+import           Data.Vector      as V (Vector, singleton, toList)
+import           Data.Vinyl       hiding (rlens, rlens')
+import           Prelude
+
+-- | Group a vector of records by a subtype of the record type.
+--
+-- @since 0.0.1.0
+groupBy :: forall ys xs f.
+           (ys ⊆ xs)
+        => Ord (Rec f ys)
+        => Vector (Rec f xs)
+        -> M.Map (Rec f ys) (Vector (Rec f xs))
+groupBy xs = M.fromListWith (<>) $ V.toList $ fmap (\x -> (rcast x, V.singleton x)) xs
+
+-- | Group a vector of records by a single field.
+--
+-- @since 0.0.1.0
+groupBy' :: forall k s y xs.
+            k ~ (s :-> y)
+         => k ∈ xs
+         => Ord y
+         => Vector (Record xs)
+         -> M.Map y (Vector (Record xs))
+groupBy' xs = M.fromListWith (<>) $ V.toList $ fmap (\x -> (view (rlens (Proxy @(s :-> y))) x, V.singleton x)) xs
+
+-- | Group a vector of records by a single field (HKD).
+--
+-- @since 0.0.1.0
+groupBy'' :: forall k s y xs f.
+             k ~ (s :-> y)
+          => k ∈ xs
+          => Functor f
+          => Ord (f y)
+          => Vector (Rec f xs)
+          -> M.Map (f y) (Vector (Rec f xs))
+groupBy'' xs = M.fromListWith (<>) $ V.toList $ fmap (\x -> (view (rlens' (Proxy @(s :-> y))) x, V.singleton x)) xs