The textbook is the first part of a set of two books intended for studying the course of algebra and began analysis in the 11th grade with specialized training in mathematics (the second part is a problem book). Distinctive features of the textbook are the available presentation of the material, a large number of detailed examples, the priority functional-graphic line, the appearance of a number of new topics. Table of Contents:Multi-member. polynomials from one variable. Multiplicities from multiple variables. Equations of higher degrees . Degrees and Roots . Degree Functions. The concept of the root nth degree from the real number. Functions of y nx, their properties and graphs. Properties of root n-th degree . Conversion of Irrational Expressions . The concept of degree with any rational indicator. Degree functions, their properties and graphs. Extracting Roots from Complex Numbers. Indicative and logarithmic functions. Indicative function, its properties and graph. Indicative Equations. Inequality . Logarithm concept. Logarithmic function, its properties and graph. Properties of logarithms. Logarithmic equations. Logarithmic inequalities . Differentiation of exponential and logarithmic functions. Original and integral . Original and indefinite integral . Defined integral. Elements of Probability Theory and Mathematical Statistics . Probability and Geometry . Independent repetitions of tests with two outcomes. Statistical methods of information processing. Gaussian curve. The Law of Large Numbers . Equations and inequalities . Systems of Equations and Inequalities . Equivalence of Equations . General Methods of Solving Equations . The Equivalence of Inequalities . Equations and inequalities with modules. Irrational Equations and Inequalities . Proof of Inequality . Equations and inequalities with two variables. Systems of Equations . Tasks with parameters.