Quantum chemistry is the application of quantum mechanics to molecules, and it demands two literacies at once: the physics of wavefunctions and the pragmatism of chemists who need numbers for real systems. The books split along that seam, and reading them in order lets each layer of approximation make sense before the next one is stacked on top.
The trap is jumping straight to computational methods without understanding what they approximate. Density functional theory and coupled-cluster only mean something once you know why the exact many-electron problem is intractable. So the path climbs deliberately: principles first, then the machinery, then the codes.
Ground yourself in the principles
Quantum chemistry by Ira Levine is the classic teaching text, patient with the mathematics and thorough on the postulates, the hydrogen atom, and approximation methods. Read it first. Molecular quantum mechanics by Peter Atkins covers the same core with more chemical intuition and is a fine companion for a second reading of any hard chapter.
Build the electronic-structure toolkit
Modern quantum chemistry by Attila Szabo and Neil Ostlund is the bridge into real methods, deriving Hartree-Fock cleanly and introducing configuration interaction and perturbation theory. It is the book most practitioners point to as the turning point. Follow it with Molecular electronic-structure theory by Trygve Helgaker and colleagues, the comprehensive reference for correlated wavefunction methods.
For the density-functional route, A chemist's guide to density functional theory by Wolfram Koch and Max Holthausen explains DFT for people who use it, while Electronic Structure by Richard Martin gives the deeper theoretical grounding. Electron Correlation in Molecules by S. Wilson sharpens the central problem of correlation itself.
Reach for the harder theory and the codes
The quantum mechanics of many-body systems by D. J. Thouless supplies the many-body physics perspective that underlies advanced methods. Then turn practical: Introduction to Computational Chemistry by Frank Jensen and Essentials of Computational Chemistry by Christopher Cramer teach how the theory becomes actual calculations, basis sets, and running jobs.
Read in this order and the acronyms stop being magic. Follow the full path to hold the sequence together.