In this chapter, we introduce and study some of the most important classes of modules: free modules, projective modules, simple modules, semisimple modules, noetherian modules, artinian modules, modules of finite composition length. During the study of these seven classes of modules, we have the opportunity of touching several fundamental topics in Algebra, like Universal Properties, free algebraic structures, IBN rings, exact sequences of modules, splitting exact sequences, tensor product of a right module and a left module, tensor product of module morphisms, hereditary rings, of which the ring of integer is the main example, the relation between idempotent elements and direct-sum decompositions, the structure of modules over a factor ring \(R/I\) , series of modules, refinements of series of modules, equivalence of series of modules, the Schreier-Zassenhaus Theorem, and the Jordan-Hölder Theorem for modules of finite composition length.