Metric-Affine Theories of Gravity

General Relativity is not the end of the story. Several issues, ranging from Quantum Gravity to the Dark Side of the Universe need to be addressed in a self-consistent theory. Here we want to summarize some of these approaches. In particular, we want to show that the same theory, General Relativity, can be represented in different ways. This fact is questioning the basic foundations of the theory like the Equivalence Principle, the Lorentz Invariance, and so on. According to this picture, new possibilities can be taken into account in view of further theoretical and experimental developments. Topics of this chapter are more advanced with respect to the rest of the book and could be considered for some short advanced lectures.