This and the next talks will introduce the research of the chair of the group on Cluster Algebras and Quantum Groups. Cluster Algebras were invented by Fomin and Zelevinsky in the early 2000s and quickly turned into an indispensable tool in many areas of mathematics. In this talk, we will provide a gentle introduction to the subject. From the early days of the theory of cluster algebras, one of the desired constructions was to turn the quantized coordinate rings of complex simple Lie groups into quantum cluster algebras. This remained elusive. We will present a resolution of this conjecture and of the Berenstein-Zelevinsky conjecture on cluster structures on quantum double Bruhat cells. This is a joint work with Fan Qin and Hironori Oya.