In this first chapter, the basic notions about rings, modules and categories are given. For instance we give the notion of ring morphism, module morphism, functor, we describe the difference between right modules and left modules, we define bimodules, submodules and quotients. We introduce natural transformations of functors. We study direct sums and direct products of modules, We quickly recall the three Isomorphism theorems. For a module, we consider its sets of generators, its maximal submodules, and the lattice of its submodules. We construct the important example of Prüfer group.