Notes on f(R) Theories of Gravity

In this review paper we present some basic notions about f® 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® theories and the application of conformal transformations in order to show that f® 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®gravity.