The book "Elementary Stability and Bifurcation Theory" by Gérard Iooss and Daniel D. Joseph is part of the Undergraduate Texts in Mathematics series, published by Springer-Verlag Berlin Heidelberg GmbH. This second edition, expanded and simplified, covers the theory of bifurcation of asymptotic solutions of evolution problems governed by nonlinear differential equations. The authors aim to provide a general yet accessible treatment suitable for a broad audience, including engineers, biologists, chemists, physicists, mathematicians, and economists. The book is structured into several chapters, each focusing on different aspects of bifurcation and stability, such as bifurcation of steady solutions, bifurcation of periodic solutions, and bifurcation of subharmonic solutions. It emphasizes the use of power series and the Fredholm alternative to analyze bifurcation problems, avoiding advanced mathematical tools like functional analysis and topology. The authors also discuss the importance of symmetry in bifurcation theory and provide methods to simplify amplitude equations in the presence of symmetry. The second edition includes additional content on simple symmetries and introduces methods for studying stability and bifurcation in conservative systems, which were not covered in the first edition. The book concludes with a chapter on equilibrium solutions of conservative problems, leaving more complex topics in Hamiltonian systems for further study. The authors acknowledge the significant impact of modern computers on the field of stability and bifurcation theory, noting that numerical methods have made theoretical approaches more practical and comparable to observations and experiments.The book "Elementary Stability and Bifurcation Theory" by Gérard Iooss and Daniel D. Joseph is part of the Undergraduate Texts in Mathematics series, published by Springer-Verlag Berlin Heidelberg GmbH. This second edition, expanded and simplified, covers the theory of bifurcation of asymptotic solutions of evolution problems governed by nonlinear differential equations. The authors aim to provide a general yet accessible treatment suitable for a broad audience, including engineers, biologists, chemists, physicists, mathematicians, and economists. The book is structured into several chapters, each focusing on different aspects of bifurcation and stability, such as bifurcation of steady solutions, bifurcation of periodic solutions, and bifurcation of subharmonic solutions. It emphasizes the use of power series and the Fredholm alternative to analyze bifurcation problems, avoiding advanced mathematical tools like functional analysis and topology. The authors also discuss the importance of symmetry in bifurcation theory and provide methods to simplify amplitude equations in the presence of symmetry. The second edition includes additional content on simple symmetries and introduces methods for studying stability and bifurcation in conservative systems, which were not covered in the first edition. The book concludes with a chapter on equilibrium solutions of conservative problems, leaving more complex topics in Hamiltonian systems for further study. The authors acknowledge the significant impact of modern computers on the field of stability and bifurcation theory, noting that numerical methods have made theoretical approaches more practical and comparable to observations and experiments.