Essays explore modern methods of solving nonlinear differential equations, focusing on quasilinear elliptic differential equations of degenerate type, evolution variational inequalities, and multidimensional hysteresis. Material serves both as a survey of results in the field and as an introduction for non-specialists interested in applied and pure mathematics and theoretical physics. Contributions are adapted versions of a series of talks given at the July 1998 Seminar in Differential Equations, held in South Moravia. Lacks a subject index. Annotation c. Book News, Inc., Portland, OR (booknews.com)