This book presents a theory of quantum gravitation and inertia based on an original idea proposed by Nicolas Fatio de Duillier in 1690, shortly after the publication of Newton's work in 1687, Philosophiae Naturalis Principia Mathematica, giving the laws of universal gravitation and the law for the movement of bodies. It was never published nor accepted. It hypothesized that the universe was traversed by infinitely small particles interacting with matter to generate the gravitational force between two bodies. With new assumptions about the interaction between these particles and matter atoms, these interactions will be modeled using classical mechanics and then with the theory of quantum mechanics known as De Broglie-Bohm. With these these models a natural understanding of the mechanisms of gravity and inertia will be obtained. We will see why the gravitational force, although dependent on objects at a very long distance, acts instantaneously on bodies. The "standard model" of quantum mechanics introduced the notion of particles called "gravitons", supposed to be the intermediaries between two distant bodies, to create the gravitational force between them. The particles of Nicolas Fatio's aether and the gravitons of this "standard model" are considered to be one and the same entity. In parallel with the presentation of this theory, this book traces the evolution of ideas on gravitation and inertia over the ages, from antiquity to the present day.