This user-friendly work presents perturbation theory for the solution of algebraic and differential equations, especially ordinary differential equations. It covers all of the methods commonly used in both regular and singular perturbations: Taylor series, Lindstedt series, strained parameters, multiple scales, averaging, matching and WKB methods. Its unique feature is the attention given to the interpretation of results. Considerable attention is given to the mathematical validity of the methods presented and to the estimation of error in a perturbation approximation. Makes accessible to all users of perturbations theory many of the subtler points often known only by specialists.