The book successively sets out numerical methods for solving systems of linear algebraic equations, matrix inversion, complete and partial algebraic eigenvalue problems; algorithms for orthogonal and singular matrix decomposition are considered, as well as methods for solving nonlinear scalar equations and systems of such equations. Ideas, conclusions, rationale and interconnection of methods are shown, their effectiveness and features of implementations are discussed. The methods are illustrated by numerical examples. There are tasks for exercises and laboratory work.