diff --git a/cachematrix.R b/cachematrix.R
index a50be65aa44..b90428fd467 100644
--- a/cachematrix.R
+++ b/cachematrix.R
@@ -1,15 +1,69 @@
-## Put comments here that give an overall description of what your
-## functions do
-
-## Write a short comment describing this function
+#
+# Caching the Inverse of a Matrix
+#
+# Matrix inversion is usually a costly computation and their may be some benefit to caching the 
+# inverse of a matrix rather than compute it repeatedly.
+#
+# Functions:
+#
+# 1.- makeCacheMatrix: This function creates a special "matrix" object that can cache its inverse.
+# 2.- cacheSolve: This function computes the inverse of the special "matrix" returned by makeCacheMatrix.
+#     If the inverse has already been calculated (and the matrix has not changed), then the cachesolve will
+#     retrieve the inverse from the cache.
+#
 
+# Create the wrapper makeCacheMatrix function which encapsulate the list of methods defined
+# to be used in the cacheSolve function (set, get, setinverse and getinverse)
 makeCacheMatrix <- function(x = matrix()) {
+    # Checking some errors
+    if(!is.matrix(x)){
+        stop("matrix expected")
+    }
+    if(nrow(x) != ncol(x)){ 
+      stop("only square matrices can be inverted")
+    }
+  
+    inverseMatrix <- NULL
+    set <- function(newMatrix) {
+      x <<- newMatrix
+      inverseMatrix <<- NULL
+    }
+  
+    get <- function() x
+    setinverse <- function(inverse) inverseMatrix <<- inverse
+    getinverse <- function() inverseMatrix
+    # Return the list of methods
+    list(set = set, get = get,
+         setinverse = setinverse,
+         getinverse = getinverse)
+}
 
+# Solve the inverse of a square matrix
+cacheSolve <- function(x, ...) {
+    # Checking if the inverse matrix is in cache
+    inverseMatrix <- x$getinverse()
+    if(!is.null(inverseMatrix)) {
+      message("getting cached inverse matrix")
+      # Return the cached matrix
+      return(inverseMatrix)
+    }
+  
+    # Calculate the inverse matrix (usually a long time operation ...)
+    data <- x$get()
+    inverseMatrix <- solve(data, ...)
+    x$setinverse(inverseMatrix)
+  
+    # Return the calculated inverse
+    inverseMatrix
 }
 
+# Checking errors
+#makeCacheMatrix(c(1))                                   # Error: matrix expected
+#makeCacheMatrix(matrix(c(1,2,3,4,5,6), nrow=2, ncol=3)) # Error: only square matrices
 
-## Write a short comment describing this function
+# Practical example
+mdat <- matrix(c(1, 2, 11, 12), nrow = 2, ncol = 2)
+matrix1 <- makeCacheMatrix(mdat)
+cacheSolve(matrix1)
+cacheSolve(matrix1)
 
-cacheSolve <- function(x, ...) {
-        ## Return a matrix that is the inverse of 'x'
-}