The monograph outlines the elements of the theory of splines based on two approaches: the regularization method of A. N. Tikhonov and the definition of a spline as a smoothly glued piece function. General conditions for optimality (in order) of methods for solving a wide class of linear and nonlinear incorrect approximation theory problems were found, which made it possible to theoretically substantiate the optimal properties of the regularization method A.N. Tikhonov and, in particular, with discrete information assignment - the optimal properties of the splines method.