Título: Modified F(R)-gravity: an alternative to the Dark Energy Abstract : In the present talk, it is introduced the F(R) theory, which constitutes an alternative way to explain the current cosmic acceleration. Since 1998, when the majority of the scientific community accepted the cosmic acceleration by means of the analysis of supernova data, a lot of models of dark energy have been suggested. The modification of the General Relativity avoids the need to introduce any exotic form of energy that produces a repulsive gravity interaction, and it gives a natural explanation to the cosmic acceleration. I will briefly introduce the development of such theory, and then, some cosmological solutions will be constructed. The aims and problems of this modification of the General Relativity will be discussed.