This book provides a wide overview of mathematical and engineering problems which lead to the analysis of bifurcation sets, singular points and their stability properties. The presentation emphasizes the methodology, rather than a rigorous mathematical treatment, and the approach is often heuristical. A large part of the book is devoted to the description and modeling of typical applications where bifurcation parameters occur (buckling of elastic roods, plates and shells, motion of tractor-semitrailer and of railway vehicules). As a matter of fact, the book is intended for use of engineers and applied scientists, but it may represent an useful introductory reference also for mathematicians. The most interesting aspect is the variety of problems considered in the book, including in particular statical and dynamical systems. A system is statical when the study of its equilibrium positions suffices to describe its behavior. This can be often done in terms of degenerate singular points of potential functions. A system is dynamical when transition between different rest positions must be taken into account. This leads to the study of degenerate singular points of ordinary differential equations or difference equations (for time discrete models).
The book introduces the main mathematical tools involved in the analysis of such critical objects and their possible bifurcations: determinacy, unfoldings, codimension, structural stability and so on. Finally, the book contains an extensive list of references.