diff --git a/sgd.cabal b/sgd.cabal
--- a/sgd.cabal
+++ b/sgd.cabal
@@ -1,5 +1,5 @@
 name:               sgd
-version:            0.5.0.0
+version:            0.6.0.0
 synopsis:           Stochastic gradient descent
 description:
     Stochastic gradient descent library.
@@ -42,8 +42,9 @@
       , Numeric.SGD.Type
       , Numeric.SGD.DataSet
       , Numeric.SGD.ParamSet
-      , Numeric.SGD.AdaDelta
       , Numeric.SGD.Momentum
+      , Numeric.SGD.AdaDelta
+      , Numeric.SGD.Adam
       , Numeric.SGD.Sparse
       , Numeric.SGD.Sparse.Momentum
       , Numeric.SGD.Sparse.LogSigned
diff --git a/src/Numeric/SGD.hs b/src/Numeric/SGD.hs
--- a/src/Numeric/SGD.hs
+++ b/src/Numeric/SGD.hs
@@ -51,6 +51,7 @@
   -- * SGD variants
     Mom.momentum
   , Ada.adaDelta
+  , Adam.adam
 
   -- * Pure SGD
   , run
@@ -85,8 +86,9 @@
 import qualified Pipes.Prelude as P
 import           Pipes ((>->))
 
-import qualified Numeric.SGD.AdaDelta as Ada
 import qualified Numeric.SGD.Momentum as Mom
+import qualified Numeric.SGD.AdaDelta as Ada
+import qualified Numeric.SGD.Adam as Adam
 import           Numeric.SGD.Type
 import           Numeric.SGD.ParamSet
 import           Numeric.SGD.DataSet
@@ -131,7 +133,7 @@
     -- no guarantee of seeing each training sample in every epoch.
   , reportEvery :: Double
     -- ^ How often the value of the objective function should be reported (with
-    -- `1` meaning once per pass over the training data)
+    -- @1@ meaning once per pass over the training data)
   } deriving (Show, Eq, Ord, Generic)
 
 instance Default Config where
@@ -227,7 +229,7 @@
 result pDef = fmap (maybe pDef id) . P.last
 
 
--- | Apply the given function every `k` param sets flowing downstream.
+-- | Apply the given function every @k@ param sets flowing downstream.
 every :: (Monad m) => Int -> (p -> m ()) -> P.Pipe p p m x
 every k f = do
   go (1 `mod` k)
diff --git a/src/Numeric/SGD/AdaDelta.hs b/src/Numeric/SGD/AdaDelta.hs
--- a/src/Numeric/SGD/AdaDelta.hs
+++ b/src/Numeric/SGD/AdaDelta.hs
@@ -2,7 +2,8 @@
 {-# LANGUAGE DeriveGeneric #-}
 
 
--- | AdaDelta algorithm as described in the following paper:
+-- | Provides the `adaDelta` function which implements the AdaDelta algorithm
+-- as described in the following paper:
 --
 --     * https://arxiv.org/pdf/1212.5701.pdf
 
diff --git a/src/Numeric/SGD/Adam.hs b/src/Numeric/SGD/Adam.hs
new file mode 100644
--- /dev/null
+++ b/src/Numeric/SGD/Adam.hs
@@ -0,0 +1,103 @@
+{-# LANGUAGE RecordWildCards #-}
+{-# LANGUAGE DeriveGeneric #-}
+
+
+-- | Provides the `adam` function which implements the Adam algorithm based on
+-- the paper:
+--
+--     * https://arxiv.org/pdf/1412.6980
+
+
+module Numeric.SGD.Adam
+  ( Config(..)
+  , adam
+  ) where
+
+
+import           GHC.Generics (Generic)
+
+import           Prelude hiding (div)
+-- import           Control.Monad (when)
+
+import           Data.Default
+
+import qualified Pipes as P
+
+import           Numeric.SGD.Type
+import           Numeric.SGD.ParamSet
+
+
+-- | AdaDelta configuration
+data Config = Config
+  { alpha :: Double
+    -- ^ Step size
+  , beta1 :: Double
+    -- ^ 1st exponential moment decay
+  , beta2 :: Double
+    -- ^ 1st exponential moment decay
+  , eps   :: Double
+    -- ^ Epsilon
+  } deriving (Show, Eq, Ord, Generic)
+
+instance Default Config where
+  def = Config
+    { alpha = 0.001
+    , beta1 = 0.9
+    , beta2 = 0.999
+    , eps = 1.0e-8
+    }
+
+
+-- | Perform gradient descent using the Adam algorithm.  
+-- See "Numeric.SGD.Adam" for more information.
+adam
+  :: (Monad m, ParamSet p)
+  => Config
+    -- ^ Adam configuration
+  -> (e -> p -> p)
+    -- ^ Gradient on a training element
+  -> SGD m e p
+adam Config{..} gradient net0 =
+
+  let zr = zero net0 
+   in go (1 :: Integer) zr zr net0
+
+  where
+
+    go t m v net = do
+      x <- P.await
+      let g = gradient x net
+          m' = pmap (*beta1) m `add` pmap (*(1-beta1)) g
+          v' = pmap (*beta2) v `add` pmap (*(1-beta2)) (g `mul` g)
+          -- bias-corrected moment estimates 
+          mb = pmap (/(1-beta1^t)) m'
+          vb = pmap (/(1-beta2^t)) v'
+          newNet = net `sub`
+            ( pmap (*alpha) mb `div`
+              (pmap (+eps) (pmap sqrt vb))
+            )
+      P.yield newNet
+      go (t+1) m' v' newNet
+
+
+-------------------------------
+-- Utils
+-------------------------------
+
+
+-- -- | Scaling
+-- scale :: ParamSet p => Double -> p -> p
+-- scale x = pmap (*x)
+-- {-# INLINE scale #-}
+-- 
+-- 
+-- -- | Root square
+-- squareRoot :: ParamSet p => p -> p
+-- squareRoot = pmap sqrt
+-- {-# INLINE squareRoot #-}
+-- 
+-- 
+-- -- | Square
+-- square :: ParamSet p => p -> p
+-- square x = x `mul` x
+-- {-# INLINE square #-}
diff --git a/src/Numeric/SGD/DataSet.hs b/src/Numeric/SGD/DataSet.hs
--- a/src/Numeric/SGD/DataSet.hs
+++ b/src/Numeric/SGD/DataSet.hs
@@ -1,7 +1,8 @@
 {-# LANGUAGE RecordWildCards #-}
 
 
--- | Dataset abstraction.
+-- | Provides the `DataSet` type which abstracts over the actual (IO-based)
+-- representation of the training dataset.
 
 
 module Numeric.SGD.DataSet
diff --git a/src/Numeric/SGD/Momentum.hs b/src/Numeric/SGD/Momentum.hs
--- a/src/Numeric/SGD/Momentum.hs
+++ b/src/Numeric/SGD/Momentum.hs
@@ -2,7 +2,8 @@
 {-# LANGUAGE DeriveGeneric #-}
 
 
--- | Stochastic gradient descent with momentum, following:
+-- | Provides the `momentum` function which implements stochastic gradient
+-- descent with momentum, following:
 --
 --     * http://ruder.io/optimizing-gradient-descent/index.html#momentum
 
diff --git a/src/Numeric/SGD/ParamSet.hs b/src/Numeric/SGD/ParamSet.hs
--- a/src/Numeric/SGD/ParamSet.hs
+++ b/src/Numeric/SGD/ParamSet.hs
@@ -6,9 +6,25 @@
 {-# LANGUAGE BangPatterns #-}
 {-# LANGUAGE DeriveGeneric #-}
 
+-- {-# OPTIONS_GHC -O -ddump-rule-firings #-}
 
+
+-- | Provides the class `ParamSet` which is used to represent the set of
+-- parameters of a particular model.  The goal of SGD is then to find the
+-- parameter values which minimize a given objective function.
+
+
 module Numeric.SGD.ParamSet
-  ( ParamSet(..)
+  ( 
+  -- * Class
+    ParamSet(..)
+  -- * Generics
+  , GPMap
+  , GAdd
+  , GSub
+  , GDiv
+  , GMul
+  , GNorm2
   ) where
 
 
@@ -84,6 +100,7 @@
   pmap = genericPMap
   {-# INLINE pmap #-}
 
+
   default add :: (Generic a, GAdd (Rep a)) => a -> a -> a
   add = genericAdd
   {-# INLINE add #-}
@@ -103,6 +120,18 @@
   default norm_2 :: (Generic a, GNorm2 (Rep a)) => a -> Double
   norm_2 = genericNorm2
   {-# INLINE norm_2 #-}
+
+
+{-# RULES
+"ParamSet pmap/pmap" forall f g p. pmap f (pmap g p) = pmap (f . g) p
+  #-}
+
+
+-- {-# RULES
+-- "ParamSet pmap/add/pmap" forall f g p h q. 
+--   pmap f (add (pmap g p) (pmap h q))
+--   = add (pmap (f . g) p) (pmap (f . h) q)
+--   #-}
 
 
 -- -- | 'add' using GHC Generics; works if all fields are instances of
diff --git a/src/Numeric/SGD/Type.hs b/src/Numeric/SGD/Type.hs
--- a/src/Numeric/SGD/Type.hs
+++ b/src/Numeric/SGD/Type.hs
@@ -1,3 +1,6 @@
+-- | Provides the basic `SGD` pipe type.
+
+
 module Numeric.SGD.Type
   ( SGD
   ) where
@@ -7,6 +10,6 @@
 
 
 -- | SGD is a pipe which, given the initial parameter values, consumes training
--- elements of type `e` and outputs the subsequently calculated parameter sets
--- of type `p`.
+-- elements of type @e@ and outputs the subsequently calculated parameter sets
+-- of type @p@.
 type SGD m e p = p -> P.Pipe e p m ()