  Supersymmetric quantum mechanics (SUSY QM) is a powerful tool for generating
new potentials with known spectra departing from an initial solvable one. In
these lecture notes we will present some general formulas concerning SUSY QM of
first and second order for one-dimensional arbitrary systems, and we will
illustrate the method through the trigonometric Poschl-Teller potentials. Some
intrinsically related subjects, as the algebraic structure inherited by the new
Hamiltonians and the corresponding coherent states will be analyzed. The
technique will be as well implemented for periodic potentials, for which the
corresponding spectrum is composed of allowed bands separated by energy gaps.
