Classical non-rel: Lagrangian, Hamiltonian, Hamilton-Jacobi.
Classical rel: same. Also whole theory of free EM Fields and free GR fields e.g. Schwarzschild.
Quantum non-rel: Schrodinger, Heisenberg, BRST.
Quantum rel: KG equation, Dirac equation, there is one for every spin above this.... Also free KG field, free Dirac field, free EM field, etc...