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Stability theory began in the early 1960s with the work of Michael Morley, and progressed in the 1970s through Shelah's research in model-theoretic classification theory. In the mid-1990s, stability theory both influences and is influenced by number theory, algebraic group theory, Riemann surfaces and representation theory of modules. The aim of this text is to provide students with a quick route from basic model theory to research in stability theory, and to give an introduction to classification theory with an exposition of Morley's categoricity theorem.