This up-to-date text for advanced physics undergraduates and first year graduate students focuses on that portion of quantum theory which is based on the Schrödinger wave equation. Key topics rarely found in quantum mechanics texts are included, such as chapters on the hydrodynamic formulation of wave mechanics, and the Wigner function. The work also discusses properties of quantum theory in terms of classical concepts. The first two chapters concentrate on the development of quantum theory, including the various pathways which led to the discovery of quantum mechanics and the human factors involved. Then, building upon this firm historical foundation, the authors discuss the solutions of the Schrödinger equation, the most basic tool for the quantum approach to almost all of the problems of the physical states of atoms and molecules. The hydrodynamic interpretation is elaborated and the text concludes with physical and mathematical appendices, and a comprehensive bibliography with references to both historically significant and contemporary review articles.