Content -- One Quantum SL(2) -- I Preliminaries -- II Tensor Products -- III The Language of Hopf Algebras -- IV The Quantum Plane and Its Symmetries -- V The Lie Algebra of SL(2) -- VI The Quantum Enveloping Algebra of sl(2) -- VII A Hopf Algebra Structure on Uq(sl(2)) -- Two Universal R-Matrices -- VIII The Yang-Baxter Equation and (Co)Braided Bialgebras -- IX Drinfeldโs Quantum Double -- Three Low-Dimensional Topology and Tensor Categories -- X Knots, Links, Tangles, and Braids -- XI Tensor Categories -- XII The Tangle Category -- XIII Braidings -- XIV Duality in Tensor Categories -- XV Quasi-Bialgebras -- Four Quantum Groups and Monodromy -- XVI Generalities on Quantum Enveloping Algebras -- XVII Drinfeld and Jimboโs Quantum Enveloping Algebras -- XVIII Cohomology and Rigidity Theorems -- XIX Monodromy of the Knizhnik-Zamolodchikov Equations -- XX Postlude A Universal Knot Invariant -- References

1. Mathematics
2. K-theory
3. Quantum physics
4. Quantum computers
5. Spintronics
6. Mathematics
7. K-Theory
8. Quantum Physics
9. Quantum Information Technology
10. Spintronics