  The titular, foundational work of Beilinson not only gives a technique for
gluing perverse sheaves but also implicitly contains constructions of the
nearby and vanishing cycles functors of perverse sheaves. These constructions
are completely elementary and show that these functors preserve perversity and
respect Verdier duality on perverse sheaves. The work also defines a new,
"maximal extension" functor, which is left mysterious aside from its role in
the gluing theorem. In these notes, we present the complete details of all of
these constructions and theorems.
