The most complete tutorial on the application of the last five versions of the powerful computer mathematics system Maple 1011121314 in mass mathematical analytical and numerical calculations and in their graphical visualization. The book describes solutions of algebraic, differential and other equations, problems of mathematical analysis and data processing, integral transformations, calculation of special functions and the basics of mathematical modeling. The basics of programming systems are given, their extension packages, GUI GUI tools, maplets are described. The publication can serve as a user guide for Maple systems of different versions and will be useful for scientific and technical workers, engineers, graduate students, as well as students and teachers of universities and universities.