For the first time, the monograph describes the use of the three latest versions of Mathematica 5.1, 5.2 and 6.0 - the world leader among universal computer mathematics systems. Particular attention is paid to the description of the capabilities of the latest Mathematica 6.0 system, in the kernel of which about a thousand new functions have been added. For the first time, tools for dynamic evaluation of variables, advanced visualization of any type of computing and the dynamic interface of laptops (documents) are described. Many hundreds of practical examples of the use of the system in mathematical and scientific-technical calculations are given. External enhancement packages for signal and image processing and wavelet techniques are described. For all PC users using mathematical methods in education, in engineering practice and in scientific calculations.