Here are some notes and videos. You won't learn quantum field theory just from watching them, but they can accompany a course or a self-study program, if you get Schwartz's book, Zee, or one of the many other books I refer to in the videos. I want to thank Michael Haack for help.
Notes:
Possibly useful mathematics:
M1. Green's functions
M2. Differential forms and cohomology
M3. Geometry and ODEs
M4. Dynamical systems
M5. Riemann surfaces
M6. Kronecker's limit formulas