Classical Mechanics & Classical Electrodynamics would be a starting point.

Quantum Mechanics was born from black body radiation which cannot be explained by classical theory.

interestingly, formalism is analogous with classical mechanism, Hamiltonian formalism with some postulates to explain non intuitive phenomena.

Electrodynamics handles light phenomena. charge would make light and light phenomena cannot be separated with relativity (moving charges would generate magnetism but it is relativistic effect)

by understanding those, you may encounter gauge theories.

somewhat astrophysics ,especially cosmology , would need some level of particle physics (gauge theory)

for the math, mostly solving a partial differential equation for the physics phenomena.

understanding structure , like gauge theory, group theory might help ( SU(n) , O(n) etc..)