The book is written on the basis of a special course read for a number of years at the Novosibirsk University and the Moscow Institute of Physics and Technology .. The main sections in the textbook are devoted to: description of the main projection (including variational) algorithms in Hilbert spaces ; Finite Functions and Approximation Theory ; projection-network schemes and convergence theory; the method of integral identities in the projection formulation and obtaining projection-grid schemes based on it ; solving some problems of mathematical physics by the projection-grid method. For undergraduate students in Applied Mathematics, as well as for specialists in the field of applied mathematics .