The provided text is the preface and table of contents for the second edition of "Elements of Applied Bifurcation Theory" by Yuri A. Kuznetsov. The book is designed for advanced undergraduate or graduate students in mathematics and professionals in various fields who use dynamical systems as modeling tools. It covers the basic topics of bifurcation theory, including topological equivalence, codimension, and the analysis of various bifurcations in both continuous-time and discrete-time dynamical systems. The second edition updates the content to incorporate recent theoretical developments, particularly new and improved numerical methods for bifurcation analysis. Key additions include detailed normal form analyses, explicit formulas for critical normal form coefficients, and the introduction of the Melnikov integral for verifying the regularity of manifold splitting under parameter variations. The book also includes updated software reviews and corrections to misprints and minor errors. The preface highlights the book's focus on practical applications and numerical implementation, making it a valuable resource for researchers and students in applied mathematics and related fields.The provided text is the preface and table of contents for the second edition of "Elements of Applied Bifurcation Theory" by Yuri A. Kuznetsov. The book is designed for advanced undergraduate or graduate students in mathematics and professionals in various fields who use dynamical systems as modeling tools. It covers the basic topics of bifurcation theory, including topological equivalence, codimension, and the analysis of various bifurcations in both continuous-time and discrete-time dynamical systems. The second edition updates the content to incorporate recent theoretical developments, particularly new and improved numerical methods for bifurcation analysis. Key additions include detailed normal form analyses, explicit formulas for critical normal form coefficients, and the introduction of the Melnikov integral for verifying the regularity of manifold splitting under parameter variations. The book also includes updated software reviews and corrections to misprints and minor errors. The preface highlights the book's focus on practical applications and numerical implementation, making it a valuable resource for researchers and students in applied mathematics and related fields.