The aim of this publication (this paper together with several its continuations) is to present algebra as a branch of mathematics treating the contents close to the usual teaching matter. The whole exposition presupposes not a large frame of knowledge: operations with integers and fractions, square roots, removing of parentheses and other transformations of literal terms, properties of inequalities. The exposition clusters round a number of main themes: ``Number'', ``Polynomial'', ``Set'', each of which is treated in a series of chapters listed in Preface.