Quasitriangular Hopf Algebras and Yang-Baxter Equations

This is an informal introduction to the theory of quasitriangular Hopf algebras and its connections with physics. Basic properties and applications of Hopf algebras and Yang-Baxter equations are reviewed, with the quantum group U q (sl 2 ) as a frequent example. The development builds up to the representation theory of quasitriangular Hopf algebras. Much of the abstract representation theory is new, including a formula for the rank of a representation.