There is now a great interest to study general relativity (Einstein's theory of gravity) in more than the three spatial dimensions that we have observed so far and/or in more exotic spaces such as anti-de Sitter space. One of the reasons is the gauge/gravity correspondence which states that general relativity in anti-de Sitter space is equivalent to certain gauge theories similar (in some respects) to the Standard Model of particle physics. What is remarkable about this correspondence is that it allows to study these gauge theories in a regime where they are strongly interacting and traditional methods in field theory do not work. Indeed, according to the correspondence, it is precisely in this strongly interacting regime that these gauge theories can be described by classical general relativity. In fact, this correspondence has been extended to study certain condensed matter systems of great practical interest such as superconductors. However, solving the equations of general relativity analytically in general is very hard and in order to make progress I will use numerical methods. The most exciting aspect of my research proposal will be to study time-dependent processes that involve black holes in higher dimensional anti-de Sitter spaces. This is very interesting because such processes describe equilibration phenomena in strongly interacting gauge theories and they cannot be studied using standard methods. Moreover, there is a great need to understand such processes since they are directly relevant in certain collisions of particles that currently take place at the LHC. However, this area of research is very novel and therefore I will also have to develop new methods to carry out the calculations. Important as they may be, it turns out that black holes in such higher dimensional/exotic spaces may be unstable. Moreover, these instabilities hold important clues about the nature of gravity itself as described by general relativity and they may have applications to particle physics. Therefore, another major goal of my research will be to understand the instabilities (and their endpoints) that arise when studying gravity beyond the usual astrophysical setting. According to the gauge/gravity correspondence, stationary black holes describe finite temperature equilibrium configurations of these theories of particles, but we do not have a good understanding of them. What kinds of black holes exist in these exotic spaces that are relevant for the correspondence? What shapes can they have? What are the implications for these theories of particles? These are open questions that I am going to address in my research by constructing new classes of black holes and, equally important, developing general methods to find them. This project addresses fundamental questions in gravity, some of which are also highly relevant for gauge theories similar to the Standard Model. My research should lead to a better understanding of gravity, which is the force that governs the Universe at large distances, and also of gauge theories, which govern the Universe at small distances.