This book is based on a quantum course taught by the author to graduate students (Ms and PhD) at the Physics Department, College of Science, Baghdad University, Iraq, for the period 1978–2007. Also, it is based on the author's experiences as a researcher and administrator to certain research institutions and scientific organizations. It describes the quantum mechanics as a good tool to deal with studying of the properties of the microsystems (molecules, atoms, nucleus, nuclear particles, subnuclear particles, etc.). Therefore, this book in general deals with the following: 1. The Concept of the Quanta, Plank Experiment 2. Duality Property, De Broglie Hypothesis 3. Photoelectric Effect 4. Double Slits Experiment 5. Wave Mechanics and Schrödinger Equations 6. Heisenberg Concept of the New Mechanics Using the Matrix Concept 7. The Schrödinger and Heisenberg Pictures 8. The Interaction Picture 9. The Theory of Transformation 10. The Operator of Transformation 11. The Generator of the Operator of Rotation 12. The Scattering Theory 13. The Addition of Angular Momenta 14. The Approximation Methods 15. Basic Elements of Relativistic Quantum Mechanics 16. The Introduction to the Field Theory 17. Appendix A: Properties of Delta Function 18. Appendix B: Whitticker Equation Solution 19. Appendix C: Solved Problems