  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.
