Parallel implementation of algorithms involves many difficult problems. In particular among them are round-off analysis, the way to convert sequential programs and algorithms into the parallel mode, the choice of appropriate or optimal computer architect and so on. To solve these problems, it is necessary to know very well the structure of algorithms. This book deal with the mathematical mechanism that permits us to investigate structures of both sequential and parallel algorithms. This mechanism allows us to recognize and explain the relations between different methods of constructing parallel algorithms, the methods of analysing round-off errors, the methods of optimizing memory traffic, the methods of working out the fastest implementation for a given parallel computer and other methods attending the joint investigation of algorithms and computers.