>>13704552All you need to take away is
Action principles and variations of functionals
Euler Lagrange equations (first and second kind, ie also lagrange multiplicators)
Phase space and generalized coordinates (ideally in differential geometric terms)
(Legendre transform)
Hamiltonian mechanics
Poisson brackets and a little bit of symplectic geometry
Canonkcal transformations
Noether theorem
And maybe electromagnitism in covariant form
These are the basics, apply them to the most simple and important cases ie free particle, central potential, pendulum, rotator and maybe for fun stuff like euler disk
Then you can turn to the more advanced stuff like
Implementing SR
Lorentz invariance
Lorentz force from action principle
Hamilton jacobi theory
Field theory from action principles, EL eqs for fields
gauge invariance
etc etc
Almost any standard literature on the topics is good. Id have a look at the scripts of professors from cambridge, goldstein book, literally any script from a good professor will do it
Keep calm its a very fun topic and will give you extremely powerful tools and a new angle to look at physics (not just mechanics)
