The book is the second edition of a text, which was published in 1991. The text was revised and new material was added (e.g., basics of the wavelet theory, including a comparison of the Fourier and Haar series on an example). The main aim of the author was to write a book, which should be sufficiently rigorous as well as attractive for students. Its style is very different from usual calculus books: things are presented carefully with rigorous proofs but still in a different way than in monographs on similar subjects. The book contains many well-chosen examples and each of 15 chapters is followed by almost 500 exercises. More demanding exercises are marked but even unmarked ones contain deeper results (e.g., countability of the set of discontinuities of the first kind or the Dini theorem on uniform convergence). Illustrative pictures are instructive and the design of the book makes its reading a real pleasure. The book can be recommended for university libraries, teachers and students as well.