Preface Introduction Symmetric functions Schur functions and their generalizations Jacobi polynomials attached to root systems Constant term identities References Chapter 1.Symmetric Functions 1.The ring of symmetric functions 2.Monomial symmetric functions 3.Elementary symmetric functions 4.Complete symmetric functions 5.Power sums 6.Scalar product 7.Schur functions 8.Zonal polynomials 9.Jack's symmetric functions 10.Hall-Littlewood symmetric functions 11.The symmetric functions Pλ(q, t) 12.Fhrther properties of the Pλ(q, t) Chapter 2.Orthogonal Polynomials 1.Introduction 2.Root systems 3.Orbit sums and Weyl characters 4.Scalar product 5.The polynomials Pλ 6.Proof of the existence theorem 7.Proof of the existence theorem, concluded 8.Some properties of the Pλ 9.The general case Chapter 3.Postscript 1.The affine root system and the extended affine Weyl group 2.The braid group 3.The affine Hecke algebra 4.Cherednik's scalar product 5.Another proof of the existence theorem 6.The nonsymmetric polynomials Eλ 7.Calculation of (Pλ, Pλ) 8.The double affine Hecke algebra and duality 9.The Fourier transform 10.The general case References