Symmetries of Di erential Equations

Here we will provide an overview of the method of nding symmetries of partial di erential equations. First we will discuss some basic facts regarding local groups of transformations, symmetries of algebraic equations and group actions on functions. We will then proceed to a discussion of how to interpret the task of solving a PDE in terms of jet spaces, and the meaning of group actions in this setting. Finally, we will illustrate the method of nding symmetries by outlining an example. Complete proofs for every claim will not be provided. Instead we will give general outlines and the important relevant facts.