Book "Mathematical analysis. Functions, limits, series, continued fractions" opens a series of reference books on various sections of classical and modern mathematics. This issue of the Reference Mathematical Library (SMB) series, together with the next one on differentiation and integration operations, covers the main part of the material "presented in large courses, mathematical analysis. This issue includes general questions of the theory of continuous functions of one and several variables (together with the geometric base of this theory), the theory of limit transition for sequences of numbers and vectors, as well as the theory of numerical non-functional series and other similar infinite processes, in particular infinite continued fractions.