  This paper is a self-contained introduction to the theory of renormalized
Reshetikhin-Turaev invariants of links defined by Geer, Patureau-Mirand and
Turaev. Whereas the standard Reshetikhin-Turaev theory of a $\mathbb{C}$-linear
ribbon category assigns the trivial invariant to any link with a component
colored by a simple object of vanishing quantum dimension, the renormalized
theory does not. We give a streamlined development of the renormalized
Reshetikhin-Turaev theory of links for the category of weight modules over the
restricted unrolled quantum group of $\mathfrak{sl}_2(\mathbb{C})$ at an even
root of unity.
