This chapter gives some important basic definitions regarding differential equations, and describes how they are classified into different types, according to their order and whether they are linear or nonlinear. Standard analytical methods for solving certain classes of differential equations are introduced, and several worked examples are included. These types of equations include first-order separable equations, first-order linear equations, and second-order linear equations with constant coefficients. This is not the main theme of this book, but it is essential background material that will be needed for the later chapters.