For Chemistry - Atkins' Physical Chemistry and Claydens' Organic Chemistry are the bibles.
Will take you from undergrad to bits of grad school. Encompassing and clear.
It was a bit harder to find as good a bible for inorganic chemistry.
Softley' Atomic Spectra and Keeler's Why Chemical Reactions Happen are phenomenal primers too but are a bit smaller in scope than the aforementioned two.
The same Atkins from above also wrote Molecular Quantum Mechanics which is also a solid text