The book deals with some of the problems of nonlinear structures. Nowadays, the nonlinear phenomena on modified ion-acoustic (mIA) waves in degenerate quantum plasmas is a topic of great interest. In this book, a rigorous theoretical investigation has been made on nonlinear propagation of mIA waves in an unmagnetized, collisionless, relativistic, degenerate plasma with heavy positive ions. This plasma system is assumed to contain relativistic degenerate electron and positron fluids, non-relativistic degenerate positive and negative ions, and positively charged static heavy ions. The Korteweg-de Vries (K-dV), the modified K-dV, the modified Gardner and the modified Burgers equations are derived by the reductive perturbation method. The properties of different nonlinear structures, viz. solitary waves, shock waves, and DLs are systematically investigated. The basic features of the mIA waves are found to be significantly modified by the various charge state of heavy ions and the plasma particle number densities. The implications of our results in space and interstellar compact objects like non-rotating white dwarfs, neutron stars and so on have been pin-pointed in this book.