Bifurcations and Catastrophes : Geometry of Solutions to Nonlinear Problems Based on a lecture course at the Ecole Polytechnique (Paris) this text gives a rigorous introduction to many of the key ideas in nonlinear analysis dynamical systems and bifurcation theory including catastrophe theory. Wherever appropriate it emphasizes a geometrical or coordinate free approach which allows a clear focus on the essential mathematical structures. Taking a unified view it brings out features common to different branches of the subject while giving ample references for more advanced or technical developments