This paper concerns the interaction between group theory and classical mechanics in general and with the application of this theory to plasma physics in particular.
Mechanics has had a profound role in the historical development of mathematics. Leading original thinkers in pure mathematics such as Newton, Euler, Lagrange, Jacobi, Laplace, Cauchy, Gauss, Riemann, Poincaré, Hilbert, Birkhofï, Smale and Arnold were also great original thinkers in various facets of mechanics. The interaction between mechanics and pure mathematics remains one of the most active and flourishing areas of current research. It is this flavor which I hope to convey in this lecture.
