The most complete self-taught application of the five latest versions of the powerful computer mathematics system Maple 10/11/12/13/14 in mass mathematical analytical and numerical calculations and in their graphical visualization. The book describes the solutions of algebraic, differential and other equations, problems of mathematical analysis and data processing, integral transformations, the calculation of special functions and the basis of mathematical modeling. The basics of system programming are given, their expansion packages, GUI graphical user interface tools, maplets. are described. The publication can serve as a user's guide to Maple systems of different versions and will be useful to scientific and technical workers, engineers, graduate students, as well as students and teachers of universities and universities.