  This article serves a two-fold purpose. On the one hand, it is a survey about
the classification of finite-dimensional pointed Hopf algebras with abelian
coradical, whose final step is the computation of the liftings or deformations
of graded Hopf algebras. On the other, we present a step-by-step guide to carry
out the strategy developed to construct the liftings. As an example, we
conclude the work with the classification of pointed Hopf algebras of type
$B_2$.
