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diff --git a/README.md b/README.md
index 1d6f5bd..3df18f5 100644
--- a/README.md
+++ b/README.md
@@ -1,15 +1,15 @@
 
-#Introduction#
+# Introduction #
 
-This package implements a new module nn.DAG which inherits from
-nn.Container and allows to combine modules in an arbitrary graph
-without cycle.
+This package implements a new module nn.DAG for the [torch framework](https://torch.ch),
+which inherits from [nn.Container](https://github.com/torch/nn/blob/master/Container.lua) and allows to combine modules in an
+arbitrary [Directed Acyclic Graph (DAG).](https://en.wikipedia.org/wiki/Directed_acyclic_graph)
 
-##Example##
+## Example ##
 
 A typical use would be:
 
-```Lua
+```lua
 model = nn.DAG()
 
 a = nn.Linear(100, 10)
@@ -48,58 +48,59 @@ Note that DAG:connect allows to add a bunch of edges at once. This is
 particularly useful to add anonymous modules which have a single
 predecessor and successor.
 
-#Usage#
+# Usage #
 
-##Input and output##
+## Input and output ##
 
 The DAG can deal with modules which take as input and produce as
 output tensors and nested tables of tensors.
 
 If a node has a single predecessor, the output of the latter is taken
-as-is as the input of the former. If it has multiple predecessors, all
+as-is as the input to the former. If it has multiple predecessors, all
 the outputs are collected into a table, and the table is used as
-input. The indexes of the outputs in that table reflects the order in
-which the edges where created in the DAG:connect() commands.
+input. The indexes of the outputs in that table reflect the
+chronological order in which the edges where created in the
+DAG:connect() commands.
 
 The input to the DAG (respectively the produced output) is a nested
 table of inputs reflecting the structure of the nested table of
-modules provided to DAG:setInput (respectively DAG:setOutput)
+modules given as argument to DAG:setInput (respectively DAG:setOutput)
 
 So for instance, in the example above, the model expects a tensor as
 input, since it is the input to the module a, and its output will is a
 table composed of two tensors, corresponding to the outputs of d and e
 respectively.
 
-##Functions##
+## Functions ##
 
-###nn.DAG()###
+### nn.DAG() ###
 
 Create a new empty DAG, which inherits from nn.Container.
 
-###nn.DAG:connect([module1 [, module2 [, ...]]])###
+### nn.DAG:connect([module1 [, module2 [, ...]]]) ###
 
 Add new nodes corresponding to the modules passed as arguments if they
-are not already existing. Add edges between every two nodes
-corresponding to a pair of successive modules in the arguments.
+have not been already added in a previous call. Add edges between
+every two nodes associated to two successive modules in the arguments.
 
-Calling it with n > 2 arguments is strictly equivalent to calling it
-n-1 times on the pairs of successive arguments.
+Calling this function with n > 2 arguments is strictly equivalent to
+calling it n-1 times on the pairs of successive arguments.
 
-###nn.DAG:setInput(i)###
+### nn.DAG:setInput(i) ###
 
 Defines the content and structure of the input. The argument should be
 either a module, or a (nested) table of modules. The input to the DAG
 should be a (nested) table of inputs, with the corresponding structure.
 
-###nn.DAG:setOutput(o)###
+### nn.DAG:setOutput(o) ###
 
 Similar to DAG:setInput().
 
-###nn.DAG:print()###
+### nn.DAG:print() ###
 
 Prints the list of nodes.
 
-###nn.DAG:saveDot(filename)###
+### nn.DAG:saveDot(filename) ###
 
 Save a dot file to be used by the Graphviz set of tools for graph
 visualization. This dot file can than be used for instance to produce