diff --git a/cachematrix.R b/cachematrix.R
index a50be65aa44..c4a87a385f3 100644
--- a/cachematrix.R
+++ b/cachematrix.R
@@ -1,15 +1,79 @@
 ## Put comments here that give an overall description of what your
 ## functions do
 
-## Write a short comment describing this function
+## makeCacheMatrix and cacheSolve is a pair of functions that could save 
+## to compute again the inverse of a matrix which inverse has already been computed.
+## Computing an inverse of a matrix can be time consuming. Hence it ia advantageous 
+## to save the result.
+## The function makeCacheMatrix stores and retrives the matrix and its inverse.
+## The function cacheSolve computes the inverse of the matrix.
+##
+##
+# Usage:
+# > M <- matrix(c(1,2,3,4),2,2)   # Create a matrix
+# > NN <- makeCacheMatrix()       # Create an object where to store the matrix and its inverse
+# > NN$set(M)                     # Store the matrix in the object
+# > NN$get()                      # Retrieve the matrix
+#      [,1] [,2]
+# [1,]    1    3
+# [2,]    2    4
+# > NN$getinverse()               # Retrieving the inverse of a matrix not yet stored
+# NULL                            #         returns a NULL
+# > cacheSolve(NN)                # Compute the inverse of the matrix, 
+#      [,1] [,2]                  #         it automatically sotores it in the object
+# [1,]   -2  1.5
+# [2,]    1 -0.5
+# > NN$getinverse()               # Retrieving the inverse matrix form the object 
+#      [,1] [,2]                  #         now returns something meaningfull
+# [1,]   -2  1.5
+# [2,]    1 -0.5
+# > cacheSolve(NN)                # when computing, for the second time, the inverse of the 
+# getting cached data             #         same matrix, we get it straight form the cache.
+#      [,1] [,2]                  
+# [1,]   -2  1.5
+# [2,]    1 -0.5
 
+## The function makeCacheMatrix stores and retrieves the matrix and its inverse
 makeCacheMatrix <- function(x = matrix()) {
+    inverse_matrix <- NULL
+    
+    set <- function(y) {
+    	# the makeCacheMatrix$set sets a matrix in cache
+        a_matrix <<- y
+        inverse_matrix <<- NULL
 
-}
+    }
+    
+    get <- function() a_matrix
+    	# the makeCacheMatrix$get function returns a matrix from cache
+   
+    setinverse <-  function(the_inverse_matrix) inverse_matrix <<- the_inverse_matrix
+    	# the makeCacheMatrix$setinverse sets in cache the inverse of a matrix
+    
+    getinverse <- function() inverse_matrix
+    	# the makeCacheMatrix$getinverse returns from cache the inverse of a matrix
 
+	# the makeCacheMatrix function returns a list of 4 (sub)functions	
+    list(set = set, get = get,
+        setinverse = setinverse,
+        getinverse = getinverse)
+}
 
-## Write a short comment describing this function
 
+## The function cacheSolve computes the inverse of the matrix.
 cacheSolve <- function(x, ...) {
-        ## Return a matrix that is the inverse of 'x'
-}
+    # Return a matrix that is the inverse of 'x'
+    # 'x' is a composite object built up by a call to makeCacheMatrix()
+
+    inverse_matrix <- x$getinverse()  # try to get the inverse of the matrix
+    if(!is.null(inverse_matrix)) {    # the inverse of the matrix is known and stored...
+        message("getting cached data")
+        return(inverse_matrix)        # returned it !
+    }
+
+    # if no inverse matrix is stored in x 
+    the_matrix_elements <- x$get()    # get the matrix elements 
+    inverse_matrix <- solve(the_matrix_elements, ...)  # compute its inverse
+    x$setinverse(inverse_matrix)                       # stores this computed inverse matrix 
+    inverse_matrix                                     # and returned it
+}
\ No newline at end of file