We completely classify the algebraic Appel-Lauricella functions F1in several variables, so extending the famous 1873 list of H.A. Schwarz of the algebraic Gauss hypergeometric functions. We indicate some consequences for the other Appell - Lauricella functions and extend Terada's list of functions F1with euclidean discontinuous monodromy group. One new aspect of our techniques is the intervention of certain families of abelian varieties with generalized complex multiplication type. 1992, R. Oldenbourg Verlag. All rights reserved.
