This book, "Coincidence Degree, and Nonlinear Differential Equations," is a collection of lecture notes edited by A. Dold and B. Eckmann, published as part of the Lecture Notes in Mathematics series (volume 568). The authors are Robert E. Gaines and Jean L. Mawhin. Gaines is a professor at Colorado State University, while Mawhin is a professor at the Catholic University of Louvain. The book provides an in-depth exploration of coincidence degree theory and its applications to nonlinear differential equations. It covers various topics including alternative problems, coincidence degree for perturbations of Fredholm mappings, generalized continuation theorems, two-point boundary value problems, projection methods, quasibounded perturbations, semilinear elliptic partial differential equations, periodic solutions of ordinary and functional differential equations, coincidence index and bifurcation theory, and coincidence degree for k-set contractive perturbations. The book also includes references and an index. The work is published by Springer-Verlag and is dedicated to the authors' families. It is a significant contribution to the field of nonlinear analysis and differential equations, offering a comprehensive treatment of the theory and its applications. The book is structured into twelve chapters, each addressing different aspects of coincidence degree theory and its relevance to nonlinear differential equations. It is a valuable resource for researchers and students in mathematics, particularly those interested in nonlinear analysis and differential equations.This book, "Coincidence Degree, and Nonlinear Differential Equations," is a collection of lecture notes edited by A. Dold and B. Eckmann, published as part of the Lecture Notes in Mathematics series (volume 568). The authors are Robert E. Gaines and Jean L. Mawhin. Gaines is a professor at Colorado State University, while Mawhin is a professor at the Catholic University of Louvain. The book provides an in-depth exploration of coincidence degree theory and its applications to nonlinear differential equations. It covers various topics including alternative problems, coincidence degree for perturbations of Fredholm mappings, generalized continuation theorems, two-point boundary value problems, projection methods, quasibounded perturbations, semilinear elliptic partial differential equations, periodic solutions of ordinary and functional differential equations, coincidence index and bifurcation theory, and coincidence degree for k-set contractive perturbations. The book also includes references and an index. The work is published by Springer-Verlag and is dedicated to the authors' families. It is a significant contribution to the field of nonlinear analysis and differential equations, offering a comprehensive treatment of the theory and its applications. The book is structured into twelve chapters, each addressing different aspects of coincidence degree theory and its relevance to nonlinear differential equations. It is a valuable resource for researchers and students in mathematics, particularly those interested in nonlinear analysis and differential equations.