This book comprises the second half of a quantum field theory (QFT) course for graduate students. It gives a concise introduction to advanced concepts that are important for research in elementary particle theory.  Topics include the path integral, loop expansion, Feynman rules, various regularization methods, renormalization, running couplings and the renormalization group, fixed points and asymptotic freedom, effective action, Coleman-Weinberg effective potential, fermions, the axial anomaly, QED, gauge fixing, nonabelian gauge theories, unitarity, optical theorem, Slavnov-Taylor identities, beta function of Yang-Mills theory, a heuristic derivation of asymptotic freedom, instantons in SU(N) gauge theory, theta vacua and the strong CP problem. Exercises are included and are intended for advanced graduate students or postdocs seeking to deepen their understanding of QFT.

James Cline is a professor of theoretical physics at McGill University.  He earned his Ph.D. in particle physics at Caltech, held postdoctoral positions at Ohio State University, McGill, and University of Minnesota, and has been a frequent sabbatical visitor at CERN.  His research contributions, numbering over 200, have focused on elementary particle theory and its links to cosmology and astrophysics.  He has taught at advanced schools including Les Houches and TASI.

Introduction.- The Loop Expansion.- The Feynman Rules.- Evaluation of diagrams; regularization.- Renormalization.- Other regulators.- The Quantum Effective Action.- Fermions.- The Axial Anomaly.- Abelian Gauge Theories: QED.- Applications of QED.- Nonabelian gauge theories.- Nonperturbative aspects of SU(N) gauge theory.- Homeworks.