This text is intended to provide an introduction to the standard methods that are used for the solution of first-order partial differential equations. Some of these ideas are likely to be introduced, probably in a course on mathematical methods during the second year of a degree programme with, perhaps, more detail in a third year. The material has been written to provide a general – but broad – introduction to the relevant ideas, and not as a text closely linked to a specific module or course of study. Indeed, the intention is to present the material so that it can be used as an.