Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, quantum field theory, quantum technology, and quantum information science. these topics are important to know:Fundamental ideas, wave function, Schrodinger equation, Uncertainty principle, Quantum Particle in One Dimension, Postulates of Quantum Mechanics, The one-dimensional harmonic oscillator, Quantum Interpretations, Transformations and Symmetries, Rotation Invariance and Angular Momentum, Electron spin, Addition of Angular Momentum, Approximation Methods, Atoms; Atoms in Electromagnetic fields, Time-Dependent Perturbation Theory, and Scattering Theory. 

There are many textbooks that cover the Quantum Mechanics topic we need as a physicist, but I suggest reading: Introduction to Quantum Mechanics by David J. Griffiths (Undergraduate), Quantum Physics by Stephen Gasiorowics (Undergraduate), Principles of Quantum Mechanics by R. Shanker (Graduate), Quantum Mechanics by Claude Cohen-Tannoudji, Bernard Diu, Frank Laloe (Graduate). Here, you should have a sufficient knowledge of Linear algebra and differential equations (See Page of Mathematical Methods in Physics).