Vladimir Bogachev was born in Moscow in 1961. He got the PhD at Moscow State University in 1986 and he got the degree of Doctor of Sciences in 1990. Since 1986 Vladimir Bogachev has worked at the Department of Mechanics and Mathematics of Moscow State University. The main fields of his research are measure theory, nonlinear functional analysis, probability theory, and stochastic analysis. He is a well-nown expert in measure theory, probability theory, and the Malliavin calculus, and the author of more than 100 scientific publications. His monograph ``Gaussian Measures'' (AMS, 1998) has become a widely used source. Vladimir Bogachev hs been an invited speaker and a lecturer at many international conferences and several dozen universities and mathematical institutes over the world.

Scientific awards: a medal of the Academy of Sciences of the USSR and the Award of the Japan Society of Promotion of Science.

This book provides a systematic presentation of modern measure theory as it has developed over the past century. It offers three levels of presentation: a standard university graduate course, an advanced study containing some complements to the basic course (the material of this level corresponds to a variety of special courses), and more specialized topics partly covered by more than 850 exercises. The first part of the book covers the classical theory of measure and integral, presenting the ideas that go back mainly to Lebesgue. The second part details the later development up to the recent years, covering transformations of measures, conditional measures, and weak convergence of measures. The organization of the book does not require systematic reading from beginning to end; in particular, almost all sections in the supplements are independent of each other and are directly linked only to specific sections of the main part.