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This paper is a self-contained introduction to the theory of renormalizedReshetikhin-Turaev invariants of links defined by Geer, Patureau-Mirand andTuraev. Whereas the standard Reshetikhin-Turaev theory of a $\mathbb{C}$-linearribbon category assigns the trivial invariant to any link with a componentcolored by a simple object of vanishing quantum dimension, the renormalizedtheory does not. We give a streamlined development of the renormalizedReshetikhin-Turaev theory of links for the category of weight modules over therestricted unrolled quantum group of $\mathfrak{sl}_2(\mathbb{C})$ at an evenroot of unity.

Renormalized Reshetikhin-Turaev invariants for the unrolled quantum group of $\mathfrak{sl}_2(\mathbb{C})$