A dream I have long held was to write a “treatise” on quantum gravity once the theory had been finally found and experimentally confirmed. We are not yet there. There is neither experimental support nor sufficient theoretical consensus. Still, a large amount of work has been developed over the last twenty years towards a quantum theory of spacetime. Many issues have been clarified, and a definite approach has crystallized. The approach, variously denoted, is mostly known as “loop quantum gravity.”

The problem of quantum gravity has many aspects. Ideas and results are scattered in the literature. In this book I have attempted to collect the main results and to present an overall perspective on quantum gravity, as developed during this twenty-year period. The point of view is personal and the choice of subjects is determined by my own interests. I apologize to friends and colleagues for what is missing; the reason so much is missing is due to my own limitations, for which I am the first to be sorry.

It is difficult to underestimate the vastitude of the problem of quantum gravity. The physics of the early twentieth century has modified the very foundation our understanding of the physical world, changing the meaning of the basic concepts we use to grasp it: matter, causality, space and time. We are not yet able to paint a consistent picture of the world in which these modifications taken together make sense. The problem of quantum gravity is nothing less than the problem of finding this novel consistent picture, finally bringing the twentieth century scientific revolution to an end.