Quantum mechanics forms the foundation of all modern physics‎,‎ including atomic‎,‎ nuclear‎,‎ and molecular physics‎,‎ the physics of the elementary particles‎,‎ condensed matter physics‎.‎ Modern astrophysics also relies heavily on quantum mechanics‎.‎ Quantum theory is needed to understand the basis for new materials‎,‎ new devices‎,‎ the nature of light coming from stars‎,‎ the laws which govern the atomic nucleus‎,‎ and the physics of biological systems‎.‎ As a result the subject of this book is a required course for most physics graduate students‎.‎ While there are many books on the subject‎,‎ this book targets specifically graduate students and it is written with modern advances in various fields in mind‎.‎ Many examples treated in the various chapters as well as the emphasis of the presentation in the book are designed from the perspective of such problems‎.‎ For example‎,‎ the book begins by putting the Schrodinger equation on a spatial discrete lattice and the continuum limit is also discussed‎,‎ inspired by Hamiltonian lattice gauge theories‎.‎ The latter and advances in quantum simulations motivated the inclusion of the path integral formulation‎.‎ This formulation is applied to the imaginary‎-time evolution operator to project the exact ground state of the harmonic oscillator as is done in quantum simulations‎.‎ As an example of how to take advantage of symmetry in quantum mechanics‎,‎ one‎-dimensional periodic potentials are discussed‎,‎ inspired by condensed matter physics‎.‎ Atoms and molecules are discussed within mean‎-field like treatment ‎(‎Hartree‎-Fock‎)‎ and how to go beyond it‎.‎ Motivated by the recent intense activity in condensed matter and atomic physics to study the Hubbard model‎,‎ the electron correlations in the hydrogen molecule are taken into account by solving the two‎-site Hubbard model analytically‎.‎ Using the canonical Hamiltonian quantization of quantum electrodynamics‎,‎ the photons emerge as the quanta of the normal modes‎,‎ in the same way as the phonons emerge in the treatment of the normal modes of the coupled array of atoms‎.‎ This is used later to treat the interaction of radiation with atomic matter‎.‎