Brief introductory seminar series presented to my research group (led by Bruce Bartlett), with a few guests. Our goal is to introduce quantum groups assuming little background, showing a few examples, but focusing mainly on the perspective that quantum groups give rise to link invariants through their representation category. The presentation is far from exhaustive - this topic is vast, and a thorough treatment requires little short of an entire textbook. That said, my notes include references (in pink) for each section, which should help an interested reader dive deeper. Notable omissions are the Drinfeld quantum double, the construction of quantum sl(2), and proofs of several assertions. Breakdown of talks 29/09/2023We motivate the Yang-Baxter equation, introduce universal enveloping algebras & Hopf algebras, & see our first examples of quantum groups 06/10/2023We see another example of a quantum group, show how braided Hopf algebras give Yang-Baxter equation solutions, & discuss the square of the antipode map in a Hopf algebra; finally, we define ribbon categories 13/10/2023We revise graphical calculi for various kinds of category, connect various kinds of Hopf algebra (braided, ribbon, etc) with their categories of representations, & finally show how ribbon Hopf algebras produce the Reshetikhin-Turaev link invariant