This graduate-level textbook covers the essential concepts and applications of quantum mechanics. Suitable for a one-year core course, it provides a comprehensive and modern treatment, with a focus on pedagogical clarity and abundant derivations and worked examples. The text starts by reviewing the experiments that motivated the quantum revolution, then gives a concise explanation of the requisite mathematical tools, the core postulates of quantum mechanics, and the quantum version of the Noether principle relating symmetries to conserved quantities and selection rules. In addition to the usual standard topics, it covers the coherent states of the harmonic oscillator, Landau levels for a particle in a magnetic field, unbound states for Coulomb potentials, the Wigner-Eckart theorem, entanglement, the Einstein-Podolsky-Rosen problem, hidden variables theories, Bell inequalities, Aspect experiments, vibrational and rotational states of simple molecules, Bloch wavefunctions and periodic potentials, absorption and emission of light, subsystems and open systems, generalized measurements, the Lindblad equation, decoherence, the basics of quantum information, the Dirac equation, the Feynman path integral approach, and the Aharonov-Bohm effect. Exercises are included at the end of each chapter.