V. Z. Enolskii, F. Gesztesy, and H. Holden The classical massive Thirring system revisited} (119K, LaTeX) ABSTRACT. We provide a complete treatment of algebro-geometric solutions of the classical massive Thirring system. In particular, we study Dubrovin-type equations for auxiliary divisors, consider the corresponding algebro-geometric initial value problem, and derive the theta function representations of algebro-geometric solutions of the Thirring system.