Software presented in the book contain a number of useful and effective receptions of procedural and functional programming in the Mathematica that extend the system software and allow sometimes more efficiently and easily to program the projects for various purposes. The presented tools are of interest not only as independent tools, but also contain a number of the receptions useful in practical programming in the Mathematica software, having a rather essential training character. The above software rather essentially dilates the Mathematica functionality and can be useful enough for programming of many appendices. Moreover, the MathToolBox package containing more 940 tools of various purposes with freeware license is attached to the book. The given book is oriented on a wide enough circle of the users of computer mathematics systems, researchers, teachers and students of universities for courses of computer science, mathematics, physics and many other natural disciplines.