Answer:
The main branches of classical physics include:
Classical Mechanics
Electromagnetism
Optics
Thermodynamics
As well as many other sub-branches like hydrodynamics, aerodynamics, etc.
In modern physics, there are a lot of different fields of study including:
Nuclear (Particle) Physics
Quantum Electrodynamics (QED)
Quantum Chromodynamics (QCD)
Solid state (aka Condensed matter) physics
Astrophysics
Geophysics
Biophysics
etc.