This book contains survey papers based on the lectures presented at the 3rd International Winter School Modern Problems of Mathematics and Mechanics held in January 2010 at the Belarusian State University, Minsk. These lectures are devoted to different problems of modern analysis and its applications. An extended presentation of modern problems of applied analysis will enable the reader to get familiar with new approaches of mostly interdisciplinary character. The results discussed are application oriented and present new insight into applied problems of growing importance such as applications to composite materials, anomalous diffusion, and fluid dynamics.

Introduction.- Kisil, Vladimir V.: Erlangen Program at Large: Brief Outline.- Laurincikas, A.: The Riemann zeta-function: approximation of analytic functions.- Luchko, Yury: Anomalous diffusion: models, their analysis, and interpretation.- Mityushev, Vladimir, V.: R-linear and Riemann-Hilbert problems for multiply connected domains.- Plaksa, S. A.: Commutative algebras associated with classic equations of mathematical physics.- Rogosin, Sergei V.: 2D Free Boundary Value Problems.