This is Volume IV of the text book series entitled ” Physical Chemistry: Concepts & Models”. This covers the basics and extensive application of quantum mechanics. This book has been divided into five parts. First part of this book extensively discusses some important experimental observations that cannot be explained by so called classical physics and two important characteristic features of subatomic particles- they wave-particle dually and the Heisenberg’s uncertainty principle. Old quantum theory namely the Wilson-Sommerfeld Quantization principle has also been introduced here. The second part of this volume covers the mathematical formulation of quantum mechanics based on the postulates which includes discussion of wave functions and operator algebra.