Mathematical formulas are just a convenient language for presenting ideas and methods of mathematics. These ideas themselves can be described using familiar and visual images from the surrounding life. This book, the authors of which are a wonderful popularizer of science Yu.V. Pukhnachev and a prominent mathematician Yu.P. Popov, is a kind of guide to mathematics, consisting of two parts (book one and book two). In the first book, in a lively and intelligible form, it tells about theorems, axioms and definitions, sets and maps, relations, sequences and series, functions and their properties, differential and integral calculus.