The book describes for the first time the basics of programming and application of the last three versions of the Mathematica 5 system. 1, 5. 2 and 6. 0. All of them are world leaders among universal systems of computer mathematics .. Special attention is paid to the description of the latest 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. 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