Parallel implementation of algorithms involves many difficult problems. In particular among them are round-off analysis, the way to convert sequential programmes and algorithms into parallel mode, the choice of appropriate or optimal computer architect and so on. To solve the stumbling blocks of these problems it is necessary to know the structure of algorithms very well. The book treats 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, methods to analyze round-off errors, methods to optimize memory traffic, methods to work out the fastest implementation for a given parallel computer and other methods attending the joint investigation of algorithms and computers.