Intended for a first year graduate course in quantum mechanics, this collection of topics can also be considered as a set of self-contained ``monographs for pedestrians" on the Mössbauer effect, many-body quantum mechanics, kaon physics, scattering theory, Feynman diagrams, symmetries and relativistic quantum mechanics. An unusual feature of the book is the introduction of many interesting physical problems and mathematical techniques at a much earlier level than in conventional texts. This approach enables the student to see the physical implications and useful applications of quantum theory before he has mastered the formalism in detail. It provides him with new mathematical tools at an earlier stage for use in subsequent problems. It also presents the active research physicist with a ``pedestrian" treatment of many topics without the necessity of learning the formalism.