Introduction
The Euler-Lagrange Equations and Noether's Theorem
Scalar Fields
Vector Fields
Relativistic Spinor Fields
The Quantum Theory of Free Fields
Perturbative Expansion in the φ44 Model
Renormalization
The Renormalization Group
Relativistic Invariance and the Spectral Decomposition of G(2)
Paths Integrals in QFT
The Perturbative Expansion for Non-Abelian Gauge Fields
The Simplest Supersymmetric Models
Anomalies
Appendices: Some facts about generalized functions

This textbook addresses graduate students starting to specialize in theoretical physics. It provides didactic introductions to the main topics in the theory of fields, while taking into account the contemporary view of the subject. The student will find concise explanations of basic notions essential for applications of the theory of fields as well as for frontier research in theoretical physics. One third of the book is devoted to classical fields. Each chapter contains exercises of varying degree of difficulty with hints or solutions, plus summaries and worked examples as useful. It aims to deliver a unique combination of classical and quantum field theory in one compact course