This book is a volume of the Springer Briefs in Mathematical Physics and serves as an
introductory textbook on the theory of Macdonald polynomials. It is based on a series of online
lectures given by the author at the Royal Institute of Technology (KTH) Stockholm in February
and March 2021. Macdonald polynomials are a class of symmetric orthogonal polynomials in many
variables. They include important classes of special functions such as Schur functions and
Hall-Littlewood polynomials and play important roles in various fields of mathematics and
mathematical physics. After an overview of Schur functions the author introduces Macdonald
polynomials (of type A in the GLn version) as eigenfunctions of a q-difference operator
called the Macdonald-Ruijsenaars operator in the ring of symmetric polynomials. Starting from
this definition various remarkable properties of Macdonald polynomials are explained such as
orthogonality evaluation formulas and self-duality with emphasis on the roles of commuting
q-difference operators. The author also explains how Macdonald polynomials are formulated in
the framework of affine Hecke algebras and q-Dunkl operators.
