2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/70948We give an introduction to the theory of Borcherds products and to some number theoretic and geometric applications. In particular, we discuss how the theory can be used to study the geometry of Hilbert modular surfaces.34 pages, to appear in Jahresber. Dtsch. Math. VerNumber TheoryAlgebraic Geometry11F03, 11F27, 11F41, 14C17, 14C20, 11G18, 14G40text