This book is devoted to the topological fixed point theory of multivalued mappings including applications to differential inclusions and mathematical economy. It is the first monograph dealing with the fixed point theory of multivalued mappings in metric ANR spaces. Although the theoretical material was tendentiously selected with respect to applications, the text is self-contained. Current results are presented. This book will be especially useful for post-graduate students and researchers interested in fixed point theory, and in particular, topological methods in nonlinear analysis, differential equations and dynamical systems. The content is also likely to stimulate the interest of mathematical economists, population dynamics experts as well as theoretical physicists exploring the topological dynamics.