Dr. Volodymyr Brayman received his PhD in probability and statistics from the Institute of Mathematics of National Academy of Sciences of Ukraine in 2007. He is currently an Assistant Professor at the Department of Mathematical Analysis at Taras Shevchenko National University of Kyiv. He is an expert in stochastic processes, a jury member in various mathematical competitions, and an author of numerous problems proposed at the competitions. He co-authored with Prof. Alexander Kukush a problem book titled «Undergraduate Mathematics Competitions (1995-2016)», Taras Shevchenko National University of Kyiv (ISBN 978-3-319-58672-4), published with Springer.

Prof. Andrii Chaikovskyi received his PhD in differential equations from Taras Shevchenko National University of Kyiv in 2001 and completed his postdoctoral degree in differential equations (Habilitation) in 2012. He is currently the Head of the Department of Mathematical Analysis at Taras Shevchenko National University of Kyiv. He is the author/coauthor of more than 60 research papers. His research interests include abstract differential and difference equations and approximation theory.

Dr. Oleksii Konstantinov is an Associate Professor of the Department of Mathematical Analysis at Taras Shevchenko National University of Kyiv. His research interests include Operator Theory, Mathematical Scattering Theory and Differential Operators.

Prof. Alexander Kukush received his PhD in probability and statistics from Kyiv University in 1982 and completed his postdoctoral degree in probability and statistics (Habilitation) in 1995. He is a Professor of the Department of Mathematical Analysis at Taras Shevchenko National University of Kyiv. He is the author/coauthor of more than 150 research papers and 4 books. His research interests include mathematical and applied statistics, actuarial and financial mathematics.

Prof. Yuliya Mishura received her PhD in probability and statistics from Kyiv University in 1978 and completed her postdoctoral degree in probability and statistics (Habilitation) in 1990. She is currently a Professor of the Department of Probability, Statistics and Actuarial Mathematics at Taras Shevchenko National University of Kyiv. She is the author/coauthor of more than 300 research papers and 12 books. Her research interests include theory and statistics of stochastic processes, stochastic differential equations, fractional calculus and fractional processes, stochastic [...]. Oleksii Nesterenko received his PhD in mathematical analysis from Taras Shevchenko National University of Kyiv in 2007. He is currently an Associate Professor of the Department of Mathematical Analysis of Taras Shevchenko National University of Kyiv. He is the author/coauthor of more than 10 research papers. His research interests include approximation theory.

Preface.- Banach Spaces.- Hilbert Spaces.- Continuous Linear Functionals.- Hahn - Banach Theorem.- Weak and Weak* Convergence.- Bounded Linear Operators.- Uniform, Strong and Weak Operator Convergences.- Inverse Operators.- Classes of Linear Operators in Hilbert Space.- Compact Sets and Operators.- Spectrum of Linear Operators.- Spectral Theory of Compact Operators.- Integral Equations.- Generalized Functions.- Answers, hints and solutions.- List of notations.- References.