  The purpose of this work is to present some basic concepts about the
non-linear sigma model in a simple and direct way. We start with showing the
bosonic model and the Wess-Zumino-Witten term, making some comments about its
topological nature, and its association with the torsion. It is also shown that
to cancel the quantum conformal anomaly the model should obey the Einstein
equations. We provide a quick introduction about supersymmetry in chapter 2 to
help the understanding the supersymmetric extension of the model. In the last
chapter we present the supersymmetric model and its equations of motion.
Finally we work-out the two-supersymmetry case, introducing the chiral as well
as the twisted chiral fields, expliciting the very specific $SU(2)\otimes U(1)$
case.
