This course is Physics 582-583, which will cover Quantum Field Theory. In many areas of Physics, such as High Energy Physics, Gravitation and Condensed Matter Physics, the understanding of essential physical phenomena requires the consideration of the collective effects of a large number of degrees of freedom. Quantum Field Theory is the tool as well as the language that has been developed to describe the physics of problems in such apparently dissimilar fields. The aim of this course sequence is to provide the basic tools of Field Theory to students (both theorists and experimentalists) with a wide range of interests in Physics. This is not a Condensed Matter course nor is it a Particle Physics course. The ideas and tools developed here will be used in subsequent and more specialized courses. As a prerequisite I will assume that the students have mastered the contents of the Physics 580/581 sequence on graduate level Quantum Mechanics (or equivalent). In Physics 582 we will study the basic conceptual and computational tools of quantum field theory. We will discuss the applications of these methods to several areas of Physics, such as High Energy and Condensed Matter Physics, both in the Lectures and in the Problem Sets. In Physics 583 we will discuss more advanced topics including Gauge Theories, the Renormalization Group and non-perturbative methods.