BROUWER DEGREE THEORY Continuous and Differentiable Functions Construction of Brouwer Degree Degree Theory for Functions in VMO Applications to ODEs Exercises LERAY-SCHAUDER DEGREE THEORY Compact Mappings Leray-Schauder Degree Leray-Schauder Degree for Multi-valued Mappings Applications to Bifurcations Applications to ODEs and PDEs Exercises DEGREE THEORY FOR SET CONTRACTIVE MAPS Measure of Non-compactness and Set Contractions Degree Theory for Countably Condensing Mappings Applications to ODEs in Banach Spaces Exercises GENERALIZED DEGREE THEORY FOR A-PROPER MAPS A-Proper Mappings Generalized Degree for A-Proper Mappings Equations with Fredholm Mappings of Index Zero Equations with Fredholm Mappings of Index Zero Type Applications of the Generalized Degree Exercises COINCIDENCE DEGREE THEORY Fredholm Mappings Coincidence Degree for L-Compact Mappings Existence Theorems for Operator Equations Applications to ODEs Exercises DEGREE THEORY FOR MONOTONE TYPE MAPS Monotone Type Mappings in Reflexive Banach Spaces Degree Theory for Mappings of Class (S+) Degree for Perturbations of Monotone Type Mappings Degree Theory for Mappings of Class (S+)L Coincidence Degree for Mappings of Class L - (S+) Computation of Topological Degree Applications to PDEs and Evolution Equations Exercises FIXED POINT INDEX THEORY Cone in Normed Spaces Fixed Point Index Theory Fixed Point Theorems in Cones Perturbations of Condensing Mappings Index Theory for Nonself-Mappings Applications to Integral and Differential Equations Exercises REFERENCES SUBJECT INDEX