Vladimir Bogachev, born in 1961, Professor at the Department of Mechanics and Mathematics of Lomonosov Moscow State University and at the Faculty of Mathematics of the Higher School of Economics (Moscow, Russia) is an expert in measure theory and infinite-dimensional analysis and the author of more than 200 papers and 12 monographs, including his famous two-volume treatise "Measure theory" (Springer, 2007), "Gaussian measures" (AMS, 1997), "Differentiable measures and the Malliavin calculus" (AMS, 2010), "Fokker-Planck-Kolmogorov equations" (AMS, 2015), "Topological vector spaces and their applications" (Springer, 2017), "Weak convergence of measures" (AMS, 2018) , and others. An author with a high citation index (h=34 with more than 7000 citations according to the Google Scholar), Vladimir Bogachev solved several long-standing problems in measure theory and Fokker-Planck-Kolmogorov equations. He received Award of the Japan Society for Promotion of Science and Kolmogorov's Prize of the Russian Academy of Science.

Three levels of exposition in this book oriented towards different categories of readers

ranging from graduate students and PhD students to professional researchers

Based on lectures given at Mekhmat (Department of Mechanics and Mathematics of Moscow State University), one of the top mathematical departments worldwide, with its rich traditions of teaching functional analysis

Extensive additional information is presented in complementary sections and exercises provided with detailed hints or references

Metric and Topological Spaces.- Fundamentals of Measure Theory.- The Lebesgue Integral.- Connections between the Integral and Derivative.- Normed and Euclidean Spaces.- Linear Operators and Functionals.- Spectral Theory.- Locally Convex Spaces and Distributions.- The Fourier Transform and Sobolev Spaces.- Unbounded Operators and Operator Semigroups.- Banach Algebras.- Infinite-Dimensional Analysis