The Burrows-Wheeler Transformation (BWT) is an algorithm, used in some compression algorithms. It rearranges the symbols of a too compressed string after its context. That will lead to a better cluster of symbols, which results in a better compression ratio. The BWT itself does not change the size of the string, and since it only requires memory for a single pointer and some computation time, it is almost for "free". Bzip2 is nowadays one of the standard compression algorithms which use the BWT as a core algorithm. The thesis will explain how the BWT works and explain why the other algorithms in the bzip2 perform well with the rearranged data and try to reduce the compression rate further.