Fundamentals of Mathematical Analysis. Textbook for Universities

The basis of this advanced textbook on mathematical analysis is the course that was read by the author at the Faculty of Mathematics of the Higher School of Economics. The material presented in the book has a number of differences from traditional courses. So, the ranks are introduced immediately after determining the limit of the sequence, the book includes an excursion into the elementary theory of sets (including Lemma Tsorn and its application) and into the general topology (including Kantorovo, many and P-Addic numbers) A noticeable place in the textbook is given to the analysis on the varieties, including differential forms, Stox theorem and Frobenius theorem.
The textbook will be useful to junior students of mathematical specialties, mathematics teachers, as well as everyone else interested in this science