A Theory of Fields is a new approach to a unifying fundamental theory of physics. It is based on just two postulates from which gravity and electricity emerge as fundamental concepts, resulting in a set of Field Equations. The book develops solutions of these equations and, in so doing, accounts for the existence of fundamental particles and derives the principles of classical mechanics, quantum mechanics, electromagnetism and gravitation. Travelling wave solutions lead to the existence and properties of photons. Models are proposed for the proton, neutron, kaon, pion, muon, electron and electron neutrino leading to the prediction of their shapes, sizes, inertial masses and internal structures. Predicted values for the gravitational constant and charge of the electron agree with the measured values within less than 20%. Many other topics in modern physics are also dealt with in the context of the new theory, including the nuclear force, the weak force and quarks.