This volume contains the Proceedings of 'Quantum Gravity': a series of qualified lectures of most outstanding scientists given during the XIV Course of the International School of Cosmology and Gravitation. As usual of that School, the Course was conceived for researchers at different levels of scientific maturity ranging from post-doctorate research students to well established research workers: then in every lecture you can find an introduction where a review and analysis of the main mathematical, physical and epistemological difficulties encountered at the formulations of relativistic quantum theories are expounded, ranging from relativistic quantum mechanics and quantum field theory in Minkowski and in curved space-time to the various canonical and covariant approaches to quantum gravity.