Part 1: Preliminary

Path Integral 101 / Real-Space Propagators / How to Quantize Fermions Self-Consistently / Symmetries, Redundancies, and Noether

Part 2: Wilsonian Renormalization as a Paradigm

Renormalization as Coarse Graining / Running Gauge Couplings / How the Asymptotic Freedom Salvaged Particle Physics QFT / Real-Space Renormalization / Renormalizability is a Hypothesis

Part 3: Symmetries, Geometry, and Topology

From Faddeev-Popov to BRST / Bundles, Spinors, and the Kosmann Lift / Characteristic Classes and Atiyah-Singer Indices / A Lie Algebra Primer / Instantons and Monopoles / When and How the Topology Fails You

Part 4: Continuous Anomalies

Axial Anomalies via Fujikawa / Alvarez-Gaume and Witten / Can Anomalies be Covariant? / Anomaly Descent / Diffeomorphism Anomaly Redux / Anomaly Inflow and Anomaly Matching

Part 5: Discrete Anomalies

Atiyah-Patodi-Singer Indices / Chern-Simons vs. Eta Invariant / Odd Dimensional Discrete Anomalies / Even Dimensional Discrete Anomalies / Discrete Anomaly Inflow and Dai-Freed Theorem

Part 6: Worldsheet vs Spacetime