The reference manual contains a detailed description of modern effective methods of approximate solution on computers of many important and widespread problems of computational and applied mathematics. statistical data processing, approximation of functions, numerical integration and differentiation, solutions of operator equations, including integral equations and Cauchy problems for systems of ordinary differential equations, minimization of functions and mathematical programming. Particular attention is paid to poorly developed problems, for example, the calculation of special integrals, the solution of rigid systems of differential equations, etc. For many methods, tasks and computers, assessments of their main characteristics are given: complete error in solving problems on the computer, as well as the time and memory required to implement methods on the computer. For the first time, the results on optimization of numerical methods. are systematically presented. Examples, graph tables and other information that facilitate the use of a number of methods. are given.