Quantum gravity (QG) is a field of theoretical physics that seeks to describe the force of gravity according to the principles of quantum mechanics. The current understanding of gravity is based on Albert Einstein's general theory of relativity, which is formulated within the framework of classical physics. On the other hand, the nongravitational forces are described within the framework of quantum mechanics, a radically different formalism for describing physical phenomena based on probability. The necessity of a quantum mechanical description of gravity follows from the fact that one cannot consistently couple a classical system to a quantum one. In physics, gravitational waves are ripples in the curvature of space-time which propagate as waves, travelling outward from the source. Predicted in 1916 by Albert Einstein to exist on the basis of his theory of general relativity, gravitational waves theoretically transport energy as gravitational radiation. Sources of detectable gravitational waves could possibly include binary star systems composed of white dwarfs, neutron stars, or black holes. The existence of gravitational waves is a possible consequence of the Lorentz invariance of general relativity since it brings the concept of a limiting speed of propagation of the physical interactions with it. Gravitational waves cannot exist in the Newtonian theory of gravitation, in which physical interactions propagate at infinite speed. Although gravitational radiation has not been directly detected, there is indirect evidence for its existence. For example, the 1993 Nobel Prize in Physics was awarded for measurements of the Hulse-Taylor binary system which suggest that gravitational waves are more than theoretical concept. Various gravitational-wave detectors are currently under construction or are in operation, such as The Advanced LIGO which began observations in September 2015. This book discusses the current theories, concepts and experiments that pertain to quantum gravity and gravitational waves.