At the beginning we are going to review the main physical ideas experimental that defied classical physics and led to the birth of quantum mechanics. The introduction of quantum mechanics was prompted by the failure of classical physics in explaining a number of microphysical phenomena that were observed at the end of the nineteenth and early twentieth centuries. In the second period we covered all the mathematical machinery to study quantum mechanics. The Schrodinger equation is one of the comerstones of the theory of quantum mechanics, it has the structure of a linear equation. The formalism of quantum mechanics deals with operator that are linear and wavefunctions that belong to the abstract Hilbert Space. Quantum mechanics was formulated in two different ways by Schrodinger and Heisenberg. Schrodinger's wave mechanics and Heisenberg's matrix mechanics are the representation of general formalism of quantum mechanics in continuous and discrete basis systems respectively.