diff --git a/README.markdown b/README.markdown
--- a/README.markdown
+++ b/README.markdown
@@ -3,8 +3,9 @@
 
 [![Build Status](https://secure.travis-ci.org/ekmett/semigroups.png?branch=master)](http://travis-ci.org/ekmett/semigroups)
 
+Haskellers are usually familiar with monoids. A monoid has an appending operation `<>` or `mappend` and an identity element `mempty`. A Semigroup has an append `<>`, but does not require an `mempty` element. A Monoid can be made a Semigroup with just `instance Semigroup MyMonoid`
 
-In mathematics, a semigroup is an algebraic structure consisting of a set together with an associative binary operation. A semigroup generalizes a monoid in that there might not exist an identity element. It also (originally) generalized a group (a monoid with all inverses) to a type where every element did not have to have an inverse, thus the name semigroup.
+More formally, a semigroup is an algebraic structure consisting of a set together with an associative binary operation. A semigroup generalizes a monoid in that there might not exist an identity element. It also (originally) generalized a group (a monoid with all inverses) to a type where every element did not have to have an inverse, thus the name semigroup.
 
 Semigroups appear all over the place, except in the Haskell Prelude, so they are packaged here.
 
diff --git a/semigroups.cabal b/semigroups.cabal
--- a/semigroups.cabal
+++ b/semigroups.cabal
@@ -1,6 +1,6 @@
 name:          semigroups
 category:      Algebra, Data, Data Structures, Math
-version:       0.12.0.1
+version:       0.12.1
 license:       BSD3
 cabal-version: >= 1.10
 license-file:  LICENSE
diff --git a/src/Data/List/NonEmpty.hs b/src/Data/List/NonEmpty.hs
--- a/src/Data/List/NonEmpty.hs
+++ b/src/Data/List/NonEmpty.hs
@@ -27,7 +27,9 @@
    , scanr       -- :: Foldable f => (a -> b -> b) -> b -> f a -> NonEmpty b
    , scanl1      -- :: (a -> a -> a) -> NonEmpty a -> NonEmpty a
    , scanr1      -- :: (a -> a -> a) -> NonEmpty a -> NonEmpty a
-   -- , transpose   -- :: NonEmpty (NonEmpty a) -> NonEmpty (NonEmpty a)
+   , transpose   -- :: NonEmpty (NonEmpty a) -> NonEmpty (NonEmpty a)
+   , sortBy      -- :: (a -> a -> Ordering) -> NonEmpty a -> NonEmpty a
+   , sortOn      -- :: Ord o => (a -> o) -> NonEmpty a -> NonEmpty a
    -- * Basic functions
    , length      -- :: NonEmpty a -> Int
    , head        -- :: NonEmpty a -> a
@@ -107,6 +109,7 @@
 import qualified Data.Foldable as Foldable
 import qualified Data.List as List
 import Data.Monoid (mappend)
+import Data.Ord (comparing)
 import Data.Traversable
 -- import Data.Semigroup hiding (Last)
 -- import Data.Semigroup.Foldable
@@ -544,3 +547,20 @@
 nubBy :: (a -> a -> Bool) -> NonEmpty a -> NonEmpty a
 nubBy eq (a :| as) = a :| List.nubBy eq (List.filter (\b -> not (eq a b)) as)
 
+-- | 'transpose' for NonEmtpy, behaves the same as 'Data.List.transpose'
+-- The rows/columns need not be the same length, in which case
+-- > transpose . transpose /= id
+transpose :: NonEmpty (NonEmpty a) -> NonEmpty (NonEmpty a)
+transpose = fmap fromList
+          . fromList . List.transpose . Foldable.toList
+          . fmap Foldable.toList
+
+-- | 'sortBy' for NonEmtpy, behaves the same as 'Data.List.sortBy'
+sortBy :: (a -> a -> Ordering) -> NonEmpty a -> NonEmpty a
+sortBy f = lift (List.sortBy f)
+
+-- | 'sortOn' for NonEmtpy, behaves the same as:
+--
+-- > sortBy . comparing
+sortOn :: Ord o => (a -> o) -> NonEmpty a -> NonEmpty a
+sortOn = sortBy . comparing