Lie Transformation Groups -- An Introduction to Symmetry Group Analysis of Differential Equations

Abstract: These are lecture notes of a course on symmetry group analysis of differential equations, based mainly on P. J. Olver's book 'Applications of Lie Groups to Differential Equations'. The course starts out with an introduction to the theory of local transformation groups, based on the Stefan-Sussman theory on the integrability of distributions of non-constant rank. The exposition is self-contained, pre-supposing only basic knowledge in differential geometry and Lie groups.