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Now-a-days, the study with ion-acoustic (IA) waves and associated envelope solitary waves (SWs), shock waves (SHWs) and double layers (DLs) in a quantum plasma medium is considered to be a topic of great interest since quantum plasma is a nonlinear medium and to develop quantum plasma research, it is essential to study nonlinear waves in plasma physics with quantum effect. Furthermore, it always keeps a nice relation between theoretical and experimental observations. In this book, a meticulous theoretical study has been made on IA waves in a collision-less, unmagnatized quantum plasma (composed of positively-charged heavy ion fluids, Fermi electrons, and Fermi positrons) in both planar and non-planar (cylindrical and spherical) geometries. The reductive perturbation technique is employed to derive the Korteweg-de Vries (K-dV), modified K-dV, Burgers, higher-order Burgers, and Gardner equations in order to analyze the propagation of SWs, SHWs, and DLs solutions. The theoretical works presented in this book may have important implications in describing the underlying physics of IA nonlinear waves propagating in both astrophysical and laboratory plasma environments.