Software tools presented in the book contain a number of rather useful and effective methods of procedural and functional programming in Mathematica system that extend the system software and allow sometimes much more efficiently and easily to program the objects for various purposes first of all wearing system character. The above software tools rather essentially dilate the Mathematica functionality and can be useful enough for programming of many applications above all of system character. Furthermore, the book is provided with freeware package AVZ_Package containing more than 1420 procedures, functions, global variables and other program objects. The present book is oriented on a wide enough range of users of systems of the computer mathematics, teachers and students of universities at courses of computer science, mathematics and other natural–science disciplines. Estonia:Tallinn: TRG Press, 2015, 563 p., ISBN 978–9985–9508–8–3.