Mean-field theory neglects fluctuations while the vicinity of a phase transition is typically associated with large fluctuations, needed to probe phase space to induce a change of phase. Therefore, a method is required to properly study the critical behavior. Such a procedure is discussed here. The notion of scaling and its invariance in the vicinity of a critical point is the starting point to construct the procedure, called renormalization group. Several ingredients are introduced and discussed such as the assumption that thermodynamic functions are generalized homogeneous functions of the variables that leads, under scale transformation, to relations between different quantities and to relations between critical exponents that govern the critical point vicinity. The procedure is introduced using a momentum space description, ‘a la Wilson, and a real space description introducing Migdal-Kadanoff renormalization procedures. The basic idea of both methods is that, as we approach a critical point, microscopic details lose their relevance and so small distances or large momenta degrees of freedom may be “eliminated” to obtain some effective, renormalized, description. The critical points are then obtained through the fixed points of the sequence of transformations, effectively reaching a regime of scale invariance.