  This note is a survey on the basic aspects of moduli theory along with some
examples. In that respect, one of the purposes of this current document is to
understand how the introduction of stacks circumvents the non-representability
problem of the corresponding moduli functor $\mathcal{F}$ by using the
2-category of stacks. To this end, we shall briefly revisit the basics of
2-category theory and present a 2-categorical version of Yoneda's lemma.
