This is a textbook in Quantum Mechanics designed for courses taught in Chemistry, Physics, Chemical Engineering, and Materials Science. The course is commonly taken by advanced undergraduate and first year graduate students. The book is intended to be taught in one semester or in one quarter or extended lectures, and is designed to treat the major topics in some depth. The text is challenging and includes exercises aimed to encourage thought and provide a solid grounding in the fundamentals of many aspects of quantum mechanics. It's emphasis is on a general approach that does not focus mainly on the Schrodinger representation of quantum theory, as well as a more extensive consideration of time dependent problems that is usually provided in a first graduate course. Throughout the book, a sufficient amount of mathematical detail and classical mechanics background is provided to enable readers to follow the quantum mechanical developments and analysis of physical phenomena. The book will provide a solid grounding in the fundamentals of quantum mechanics, and it explicates a variety of physical problems that are key components to understanding broad areas of physical science. This book will bring readers to the point where they can focus their future efforts on more specialized topics in quantum theory.