Notes on f(R) Theories of Gravity

In this review paper we present some basic notions about f(R) theories of gravity and some simple cosmological models derived from it. We first make an introduction to General Relativity (GR), followed by the discussion of Gibbons-York-Hawking boundary term in GR. We also discuss boundary terms in f(R) theories and the application of conformal transformations in order to show that f(R) theories can be made equivalent to GR minimally coupled with a scalar filed. In the final sections of the paper a brief review of classical Friedman and Lemaitre cosmological models is made, followed by the discussion of cosmological models derived from f(R)gravity.