The principle of least action in geometry and dynamics New variational methods by Aubry Mather and Mane discovered in the last twenty years gave deep insight into the dynamics of convex Lagrangian systems. This book shows how this Principle of Least Action appears in a variety of settings (billiards length spectrum Hofer geometry modern symplectic geometry). Thus topics from modern dynamical systems and modern symplectic geometry are linked in a new and sometimes surprising way. The central object is Mathers minimal action functional. The level is for graduate students onwards but also for researchers in any of the subjects touched in the book. TOC:Aubry Mather Theory. Mather Mané Theory. The Minimal Action and Convex Billiards. The Minimal Action Near Fixed Points and Invariant Tori. The Minimal Action and Hofers Geometry. The Minimal Action and Symplectic Geometry. References. Index