I'm looking for a comprehensive book that covers Newtonian, Lagrangian, Hamiltonian, and Relativitistic Mechanics. Is there such a book, and what is it called?
Classical Mechanics by Taylor does it too. It's simpler to understand than Goldstein, but much less rigorous. Still, if you never played with lagrangian/hamiltonian mechanics, you're better with Taylor.
And I used Hand & Finch (and recommend it as much as I can recommend any classical mechanics book, although it sort of presupposes you know enough Newtonian mechanics.)