Computer algebra packages and symbolic computation

General principles for the constraction and architecture of computer algebra packages are considered. The range of tasks that can be solved with their help is indicated. A classification of such systems is presented, and the most popular and signficant packages for symbolic computing are listed. We mention fundamental characteristics of computer algebra systems, as well as data types. A difference between symbolic computation and numerical methods is indicated. Two examples of algebraic calculations in the packages Maxima and GAP 4.2 are given. They concern the solution of nonlinear algebraic systems and the computations with subgroup lattices, respectively.