Abstract
In recent decades, an important shift has taken place with the growing role of non-Hermitian quantum mechanics. What makes this framework remarkable is that the eigenvalues of the Hamiltonians involved can still be real, just as in the Hermitian case. Before turning to non-Hermitian quantum mechanics, we will first review some basic ideas and mathematical tools from the standard Hermitian formulation. This review is intended as a survey: most results will be stated without proof and without going into detailed discussion.