I've come to a point in studying quantum mechanics where Schrodinger equation becomes a sore in the eye. Dirac introduced a much simpler notations for quantum mechanical calculations. The matrix formulation, however, is named after Heisenberg. The mathematical machinery involve in quantum mechanics are much simpler if calculated using vector-like mathematical objects, for instance the bra and ket. This leads to a formal structure of Quantum Mechanics. I hope to elucidate some kernel of knowledge regarding mathematical tools of Quantum Mechanics needed to advance to higher physics, e.g. quantum statistics, quantum field theory, superconductivity, and statistical field theory.