Abstract: A book from a series of textbooks on the course "Computer algebra" . One of the main problems of computer algebra is considered - the problem of data representation. The focus is on representations of polynomial, differential and difference modules. The corresponding methods are called Grebner's theory of bases. Several equivalent definitions of Grebner bases are formulated, algorithms for their calculation, some applications are given, among which is the calculation of the characteristic Hilbert polynomials. For students of the Faculty of Mechanics and Mathematics of Moscow State University . Other books on numerical methods on the site: Mitchell E. , Wait R. Finite element method for partial derivatives Isakov B. B. Elements of Numerical Methods Korneichuk H. P. , Babenko V. F. , Ligun A. A. Extreme properties of polynomials and splines Korneichuk N. P. Splines in the theory of approximation of Ignatov M. and . , Certain A. B. Natural splines of many variables Rogers D. Adams J. Mathematical Foundations of Machine Graphics Zaliznyak B. E. Basics of Scientific Computing . Introduction to Numerical Methods for Wolf Physicists E. Numerical methods Kalitkin N. N. Numerical methods Samara A. A. Introduction to Numerical Methods