The three lectures will survey by now classical results for BC type Jacobi polynomials and Macdonald-Koornwinder polynomials.Some new results and some directions for research suggested by low rank cases will also be given.

Here is a list of topics, on the one hand only tentative, on the other hand not necessarily exhaustive:

- Jacobi polynomials associated with root systems: the Heckman-Cherednik approach using Dunkl type operators
- Opdam's shift operators
- Jack polynomials, shifted Jack polynomials and generalized binomial coefficients
- Expansion of BC type Jacobi polynomials in terms of Jack polynomials
- Explicit results for BC_2 type Jacobi polynomials and their possible extensions to BC_n
- Macdonald polynomials associated with root systems and the Macdonald-Koornwinder (MK) case
- Double affine Hecke algebra (DAHA) and non-symmetric MK polynomials
- Limits of MK and its DAHA to q=1
- Explicit results in the rank 1 and 2 MK case and possible generalizations to general rank
- The q=0 limit (BC_n Hall-Littlewood)
- Elliptic analogue of MK polynomials.