This is the introduction to Section I/9, Algorithms and Programming, of the Encyclopaedia of Computer Science and Information Systems. This section is devoted to three fundamental tools in computer science: algorithms, machine models and programming languages. Introduced around 1950, finite automata form the most elementary model of machine. This chapter presents automata in the usual sense, that accept or reject a given word and sequential automata, that produce an output. After a brief presentation of Kleene's theorem, the cornerstone of the theory of automata, we describe applications in various domains, notably their use as a verification model and their applications to natural languages.