The roots of Homological Algebra can be traced back to the 1900s when H. Poincaré did some serious work on simplicial homology. The algebraic formalism can be attributed to S. Maclane who, in 1942, introduced the notions of category and functor. Since then these notions have become a very important part of mathematics. In this talk I will describe the derived functors Ext and Tor, on the category of R-modules, two of the basic constructions in Homological Algebra and I will present some results in connection with commutative algebra invariants.