The monograph describes for the first time the use of the last three versions of the Mathematica 5 system 1, 5. 2 and 6. 0 - world leader among universal computer mathematics systems . Special attention is paid to the description of the capabilities of the latest Mathematica 6 system. 0, in the core of which about a thousand new functions are added. For the first time described means of dynamic evaluation of variables, advanced visualization of any types of calculations and dynamic interface of laptops (documents) Many hundreds of practical examples of the use of the system in mathematical and scientific-technical calculations are given. External expansion packages for signal and image processing and wavelet application techniques are described. For all PC users using mathematical methods in education, in engineering practice and in scientific calculations