**Abstract**

Our interest in General Relativity, Cosmology and String theory remains strong. The problems did not modify in any drastic way in the last five years. Therefore, our project continues being a quest for perturbative methods in General Relativity, a study of String now more clearly related to integrable models, with which we have a good deal of experience and to the question of Dark Matter and Dark Energy, which is more clearly formulated than four years ago, the methods being better and especially more powerful. General relativity is the best suited theory describing gravitational phenomena. It is succesfully used in a vast class of situations, from the description of isolated stars, at distances typical of the solar system, all the way up until cosmology, at the largest observable distances. The study of perturbations in General Relativity is a formidable instrument to study actual problems and to comprehend the cosmos, from the structure of astrophysical objects (where, among other things, gravitational waves are predicted) until the possibility of describing physical processes at the beginning of the cosmic history. In particular, the fact that various experiments related to the observation of gravitational waves are under way (one of them in Brazil) is a strong motivation for this part of our project. Quantum Gravity, on the other hand, allows knowledge about a unified theory of all interactions, thus rendering possible the understanding of the initial explosion itself, what cannot be done in the context of General Relativity only. In this case, String theory is the correct formulation, such that we have to test its validity. One of the most important problems in this context is that of the cosmological constant, extremely small, but explaining the accelerating universe, as experimentally seen by means of the supernovae observations. Thus, we search the understanding of questions involving Einstein Gravity and its quantization, as well as its applications, together with Quantum Field Theory, in the cosmological context. The study of gravitational waves is closed related to the time evolution of small perturbations in the gravitational field of a star, a black hole, or else another large astrophysical object. Or else, as we have seen more recently, the gravitational waves can arise, more effectively, from time dependent processes, as the mass accretion into a Black Hole or a fusion of two neutron stars. Finally, we have also studied problems related to the observation of mini Black Holes as predicted for the next generation of particle acceleratos, the LHC (it Large Hadron Collider}), at CERN, Geneva. In order to probe string theory as a result of facts it foresees, which are observationally important, is the most important aim to be achieved. Thus, it is important to understand string theory solutions that play an important role in cosmology and in the formation of the universe, as well as in its description as a whole. This is done by means of the Theory of Branes. A whole series of questions are posed in such a context, in particular that of the existence of shortcuts for gravitational waves by means of passages through the extra dimensions, outside of the brane itself. Beside that, one of the most important questions is that of the description of a very small but positive cosmological constant. This implies that it is crucial to understand the de 5itter space and the Conformal Field Theory at the border of the universe. (AU)