Any recs for learning Classical Mechanics?

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I'm in my 2nd year of Physics and feel slightly silly learning about Relativity and Quantum when I haven't yet mastered Classical Mechanics. What are some good text books for developing a really deep understanding of Classical? I want to be able to easily solve hard Classical problems as well as to have an intuitive understanding of what it all means; I know the equations, but I want to understand intuitively, what is momentum, energy, etc in a Classical context. Ideally this book should introduce just a handful of axioms are reason everything out from them.