diff --git a/cachematrix.R b/cachematrix.R
index a50be65aa44..387670d1e44 100644
--- a/cachematrix.R
+++ b/cachematrix.R
@@ -1,15 +1,44 @@
-## Put comments here that give an overall description of what your
-## functions do
-
-## Write a short comment describing this function
+## The makeCacheMatrix function creates a special list object that stores a matrix and also contains a cache for its inverse. The structure is based on the example from the exercise in which the mean value of a vector was temporarily stored. This principle has been applied to matrices here.
 
 makeCacheMatrix <- function(x = matrix()) {
-
+  inv <- NULL      # Cache für die Inverse
+  
+  set <- function(y) {
+    x <<- y        # neue Matrix setzen
+    inv <<- NULL   # Cache resetten, weil Matrix sich geändert hat
+  }
+  
+  get <- function() {
+    x
+  }
+  
+  setinv <- function(inverse) {
+    inv <<- inverse
+  }
+  
+  getinv <- function() {
+    inv
+  }
+  
+  list(
+    set = set,
+    get = get,
+    setinv = setinv,
+    getinv = getinv
+  )
 }
 
-
-## Write a short comment describing this function
-
+## The cacheSolve function computes the inverse of the matrix stored inside a makeCacheMatrix object. It first checks whether the inverse is already available in the cache. If so, it returns the cached value immediately to avoid redundant computation.
 cacheSolve <- function(x, ...) {
-        ## Return a matrix that is the inverse of 'x'
+  inv <- x$getinv()
+  
+  if (!is.null(inv)) {
+    message("getting cached data")
+    return(inv)
+  }
+  
+  mat <- x$get()
+  inv <- solve(mat, ...)   # Inverse berechnen
+  x$setinv(inv)
+  inv
 }