(some) standard treatments (for physicists) are:
At the most elementary level (taken before or in parallel with a standard calculus sequence) there is for instance the The M.I.T. Introductory Physics Series by Anthony Philip French (volumes on: mechanics, electromagnetism, vibrations and waves, special relativity,...)
undergraduate (upper-level; start here if you know the math)
Goldstein Classical Mechanics, Griffiths Introduction to electrodynamics, Griffiths Quantum Mechanics, Griffiths Introduction to elementary particles, Reif Fundamentals of Statistical and Thermal Physics
Arnol'd Mathematical Methods of Classical Mechanics, Jackson Electrodynamics, Sakurai Modern Quantum Mechanics, Kardar Statistical Physics of [...] (two volumes), J.Negele H.Orland Quantum Many-particle Systems, Wald General Relativity, M.Peskin D.Schroeder, An Introduction to Quantum Field Theory ...
As well as the older series by Sommerfelt, or Landau. And the text on electrodynamics by Smythe.
Higher-level courses in mechanics is (often) geared toward teaching the math needed to study modern physics. That's one of the primary motivations. Goldstein (quantum mechanics), Arnol'd (gauge field theories) etc.