This book describes the basics of programming and applying the latest three versions of Mathematica 5 (5.1 and 5.2), 6.0 and 7.0. All of them are world leaders among universal computer mathematics systems. Particular attention is paid to the description of the most popular version of Mathematica 6.0, in the kernel of which over a thousand new functions and commands have been added, unique tools for dynamic variable evaluation, visualization of any kind of calculations and the dynamic graphical interface of laptops (documents) have been introduced.