The aim of this book is to present the fundamental concepts and properties of quantum mechanics, in particular the field of quantum optics. In this book we have studied some extensions and generalizationsof the Jaynes-Cummings model JCM for the radiation-matter interactions. We have reviewedthe JCM and its various modifications and some important quantum characteristics.The interaction of two two-level atoms with a single mode cavity field is studied. The interaction of a four-level rubidium atom and one mode field in a cavity in the presence of intensity dependent coupling between the field and the atom is presented. The interaction of a moving four-level rubidium atom with two-mode cavity field in an additional Kerr medium has been studied. Some non classical statistical properties of a model for the interaction between a four-level atom with a three-mode field in a cavity containing a Kerr-like medium are investigate.