This core course in Quantum Mechanics covers the basic Hilbert space formulation of Quantum Mechanics as well as operator algebra, representations, the Heisenberg and Schrodinger pictures, and the von-Neumann equation for density matrix. The list of other topics is as follows. Basic formalism of quantum mechanics: time-independent and time-dependent pictures; variational, perturbational, and semi-classical approaches; symmetry, representation theory; identical particles, second quantization; different boundary conditions: open and periodic systems.