In this paper, we construct abelian varieties associated to Gauss' and
Appell--Lauricella hypergeometric series.
Abelian varieties of this kind and the algebraic curves we define
to construct them were considered by several authors in settings
ranging from monodromy groups (Deligne, Mostow), exceptional sets
(Cohen, Wolfart, W\"ustholz), modular embeddings (Cohen, Wolfart) to
CM-type (Cohen, Shiga, Wolfart) and modularity (Darmon).
Our contribution is to provide a complete, explicit and self-contained