Fritz Gesztesy, Helge Holden, Johanna Michor, and Gerald Teschl Algebro-Geometric Solutions of the Ablowitz-Ladik Hierarchy (142K, LaTeX) ABSTRACT. We provide a detailed derivation of all complex-valued algebro-geometric finite-band solutions of the Ablowitz-Ladik hierarchy. In addition, we survey a recursive construction of the Ablowitz-Ladik hierarchy and its zero-curvature and Lax formalism.