This book is an introduction to the theory of discrete-time models and bifurcations, addressed to master students in economics. Time representation can be discrete or continuous. However, a discrete representation of economic transactions is more suitable since they take place at some instants of time. A common practice among economists is to study economic dynamics by means of linear approximations. Policy recommendations based on these simplifications may be misleading. The theory of bifurcations takes into account nonlinearities and sudden changes in stability induced by small perturbations, and it may help a public authority to implement more efficient policies. The book provides rigorous proofs of the main results and simple applications. Discrete and continuous-time economic models are compared in the last chapter.