Hypergeometric functions (in one and several variables) are classical functions which occur at many places in mathematics and mathematical physics. We shall be interested in hypergeometric functions which are at the same time algebraic in their arguments. This subject started in 1873 with the work of H.A. Schwarz. In this lecture we discuss a number of examples, introduce a general class of several variable hypergeometric functions, the so-called GKZ-functions, and describe a combinatorial criterion for their alegebraicity. |