This book, titled "Numerical Continuation Methods: An Introduction," is part of the Springer Series in Computational Mathematics. It is authored by Eugene L. Allgower and Kurt Georg from the Department of Mathematics at Colorado State University. The book provides an introduction to two key techniques for solving nonlinear systems of equations: the predictor-corrector or pseudo arc-length continuation method and the simplicial or piecewise linear method. These methods have been widely used in engineering and scientific computing to improve convergence properties when an initial guess is not available. The authors aim to make the numerical aspects of these methods accessible to both scientific workers and students. They discuss the commonalities and differences between the two methods, emphasizing that they are closely related despite their distinct origins. The book is structured into several chapters, with the first 10 chapters focusing on predictor-corrector methods and the next 6 chapters on piecewise linear methods. Chapter 11 bridges these approaches by discussing applications where either or both methods can be applied. The book includes pseudocodes in PASCAL for algorithms, along with FORTRAN programs and numerical examples in the appendix. The authors provide a detailed bibliography and acknowledge the support received during the preparation of the book, including funding from the National Science Foundation and the Deutsche Forschungsgemeinschaft. The book is intended for readers with a background in elementary analysis and linear algebra, and it is suitable for students and researchers in mathematics, engineering, and sciences.This book, titled "Numerical Continuation Methods: An Introduction," is part of the Springer Series in Computational Mathematics. It is authored by Eugene L. Allgower and Kurt Georg from the Department of Mathematics at Colorado State University. The book provides an introduction to two key techniques for solving nonlinear systems of equations: the predictor-corrector or pseudo arc-length continuation method and the simplicial or piecewise linear method. These methods have been widely used in engineering and scientific computing to improve convergence properties when an initial guess is not available. The authors aim to make the numerical aspects of these methods accessible to both scientific workers and students. They discuss the commonalities and differences between the two methods, emphasizing that they are closely related despite their distinct origins. The book is structured into several chapters, with the first 10 chapters focusing on predictor-corrector methods and the next 6 chapters on piecewise linear methods. Chapter 11 bridges these approaches by discussing applications where either or both methods can be applied. The book includes pseudocodes in PASCAL for algorithms, along with FORTRAN programs and numerical examples in the appendix. The authors provide a detailed bibliography and acknowledge the support received during the preparation of the book, including funding from the National Science Foundation and the Deutsche Forschungsgemeinschaft. The book is intended for readers with a background in elementary analysis and linear algebra, and it is suitable for students and researchers in mathematics, engineering, and sciences.