The book describes the basics of programming and application of the last three versions of the Mathematica 5 system (5. 1 and 5. 2), 6. 0 and 7. 0. All of them are world leaders among universal computer mathematics systems . Special attention is paid to the description of the most popular version of Mathematica 6. 0, in the core of which more than a thousand new functions and commands are added, unique means of dynamic evaluation of variables, visualization of any types of calculations and dynamic graphical interface of laptops (documents) are introduced Described hundreds of examples of the use of systems. In the last chapter added new features version 7. 0. The publication is intended for all PC users who use mathematical methods in education, in engineering practice and in scientific calculations and, above all, want to master programming in Mathematica systems.