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We use an algebraic method to compute de Haas-van Alphen oscillations in two-dimensional systems in the semiclassical approximation for cases where the Fermi surface lies on more than one sheet of the energy surface. We treat magnetic breakdown by computing the Riemann surface associated with the Bloch energy equation. The topology of this surface, in particular, its fundamental group, is used to classify electronic trajectories in the complexified Brillouin zone. Three examples taken from tight-binding models of quasi-two-dimensional organic conductors show how this can be implemented to calculate frequencies and breakdown fields.