The field of Highly Frustrated Magnetism has developed and expanded considerably over the last 15 years. Originating with canonical geometric frustration of interactions, it today extends over other phenomena with many degrees of freedom, including magneto-elastic couplings, orbital degrees of freedom, dilution effects, and electron doping. It is also demonstrated that the concept of frustration impacts many other fields in physics beyond magnetism. This book represents a state-of-the-art review aimed at a broad audience with tutorial chapters and more topical ones, which encompass solid-state chemistry as well as experimental and theoretical physics.