diff --git a/cachematrix.R b/cachematrix.R
index a50be65aa44..ff94f68be42 100644
--- a/cachematrix.R
+++ b/cachematrix.R
@@ -1,15 +1,47 @@
 ## Put comments here that give an overall description of what your
-## functions do
+## functions do:
+## finding the inverse of a (square-)matrix. If already calculated, 
+# the function looks if the result is stored in cache and gives the result
+# to unecessary computation especially for complex matrices is avoided
+
 
 ## Write a short comment describing this function
 
-makeCacheMatrix <- function(x = matrix()) {
+## this is a function that implements some functions to handle the 
+## matrix and gets and sets some properties
 
+makeCacheMatrix <- function(x = matrix()) {
+  m <- NULL
+  set <- function(y) {
+    x <<- y
+    m <<- NULL
+  }
+  get <- function() x
+  setinv <- function(inv) m <<- inv
+  getinv <- function() m
+  list(set = set, get = get,
+       setinv = setinv,
+       getinv = getinv)
 }
 
 
 ## Write a short comment describing this function
 
+# this functon calculates the inverse of a given 
+# square matrix created by the above function.
+# If calculated before and if  the result is in cache, it 
+# simply gives bach the cached result.
+# If not, the inverse is calculated and stored in cache
+
 cacheSolve <- function(x, ...) {
         ## Return a matrix that is the inverse of 'x'
+  m <- x$getinv()
+  if(!is.null(m)) {
+    message("getting cached data")
+    return(m)
+  }
+  data <- x$get()
+  m <- solve(data, ...)
+  x$setinv(m)
+  m
 }