The purpose of this preprint is two-fold. First, present the theory of sheaves with transfers of Voevodsky over a perfect field together with the proof of the main results of the theory, as for example the homotopy invariance of cohomology. Here we follow mainly the original proof of Voevodsky except that we use only the Nisnevich topology and we work with finite correspondances up to homotopy. This later fact allows to give a neat exposition of the basis for the theory. Second, establish the theory of finite correspondances over a regular base using Serre Tor formula for computing intersection multiplicities.