T h e p r e s e n t book, together with its companion volume devoted to the differential and integral calculus, contains the fundamental part of the material dealt with in the larger courses of mathematical analysis. Included in this volume are general problems of the theory of continuous functions of one and several variables (with the geometrical basis of this theory), the theory of limiting values for sequences of numbers and vectors, and also the theory of numerical series and series of functions and other analogous infinite processes, in particular, infinite continued fractions.