This course begins with a basic introduction to the fundamental postulates of quantum theory. These postulates are then used to develop Heisenberg's Uncertainty Principle and Schrodinger's equation. Solutions to Schrodinger's equation are sought, first to relatively simple systems such as square wells and harmonic oscillators, and then to the hydrogen atom. The properties of the hydrogen atom are studied in detail. The course also covers approximation methods used for physical systems with small perturbing forces acting on them.