The main goal of this course is to introduce the audience the preliminaries on quantum groups and Hopf algebras using explicit examples and the relation with algebraic geometry and category theory. In particular, it consists of examples and basic results that are the essential toolkit to study and research on topics related to quantum groups: from Hopf algebras to tensor categories. As it is an active area of research, we will take the opportunity to dscuss open problems and recent results of interest.