The book provides a quick overview of a wide range of active research areas in partial differential equations such as evolution equations and estimates for their solutions, control theory, inverse problems, nonlinear equations, elliptic theory on singular domains, numerical approaches. It will serve as a useful source of information to mathematicians, scientists and engineers. Contributors: Y.P. Apakov G. Avalos L. Bociu L. Boutet de Monvel F. Colombo G. Fragnelli M. Ghergu D. Guidetti U.U. Hrusheuski T.Sh. Kalmenov I.U. Khaydarov S. Khodjiev V. Kokilashvili C. Lebiedzik P. Loreti F. Macià D. Mugnai M. Reissig M.S. Salakhitdinov B.-W. Schulze D. Sforza L. Simon D. Suragan D. Toundykov R. Triggiani A.K. Urinov O.S. Zikirov J.-P. Zolésio