Quantum Gravity can be said as the main target of this century's high energy physics. This is a theory that would unite Quantum Mechanics and the world of the subatomic particles with General Relativity and the world of the macroscopic objects like stars, galaxies and the Universe. Despite the many dificulties in obtaining such a theory, there have been considerable progress during the last decades. Two of the most promising attempts at obtaining such a theory are String Theory, that revolutionalizes the concept of a particle and uses a perturbative formalism, and Canonical Quantization, which uses standard, non-perturbative, quantization methods, allied with Ashtekar's variables.
Both theories have strong and weak points, but if they are ever to describe the theory of Quantum Gravity, they must converge at some point. In the next topics I show how I am trying to analize this subject.