In this book, a precise theoretical investigation is made on nonlinear propagation of positron-acoustic (PA) waves in electron-positron-ion plasmas (containing nonthermal distributed hot positrons and electrons, inertial cold positrons, and immobile positive ions). The Korteweg-de Vries (K-dV), the modified K-dV, the modified Gardner, and the Burgers equations are derived by using the reductive perturbation method. The basic features of nonlinear phenomena (solitons, shocks, and double-layers) are briefly studied. The properties of the nonlinear PA waves are found to be significantly modified by the effects of nonthermality of hot positrons and electrons, relative number density and temperature ratios. The important findings of our results in astrophysical plasmas like supernova, pulsar magnetosphere, active galactic nuclei, and so on are pin-pointed in this book.