It has been conjectured that maximally supersymmetric SU(N) Yang-Mills theory is dual to a String Theory on asymptotically AdS_5 times S^5 backgrounds. This is known as the AdS/CFT correspondence. In this talk I will show how using one-loop calculations in the gauge theory, one can study the emergence of the dual String Theory. We will see, quite explicitly, the emergence of closed strings, D-branes, open strings and space-time itself. This is done in a reduced sector (SU(2) sector), where the gauge theory can be written as Matrix Quantum Mechanics. This simple sector provides a toy model of a non-perturbative quantum theory of gravity.