This will be a survey, devised mainly for non-specialists, of (some aspects of) the theory of quantum groups and its applications, and interactions with other parts of mathematics. I would like to cover (some of ) the following topics, illustrating them mainly with the example of quantum sl(2) and may be quantum linear groups.

• Hopf algebras (which provide the algebraic framework),
• Yang-Baxter equation, braid groups, link invariants (in particular the Jones polynomial),
• Classical and quantum invariant theory (Hecke algebras and their relation with quantum linear groups),
• Representation theory and relation with simple Lie algebras (over the field of complex numbers and also in finite characteristic),
• Special functions and their q-analogues.