Quantum Gravity

General lectures on quantum gravity. 1 General Questions on Quantum Gravity It is not clear at all what is the problem in quantum gravity (cf. [3] or [8] for general reviews, written in the same spirit as the present one). The answers to the following questions are not known, and I believe it can do no harm to think about them before embarking in a more technical discussion. To begin, it has been proposed that gravity should not be quantized, owing to its special properties as determining the background on which all other fields propagate. There is a whole line of thought on the possibility that gravity is not a fundamental theory, and this is certainly an alternative one has to bear in mind. Indeed, even the holographic principle of G. ’t Hooft, to be discussed later, can be interpreted in this sense. Lectures given in the 40th Karpacz Winter School.