Explore Kirchhoff's theorem and its applications to tropical Prym varieties in this 34-minute lecture by Dmitry Zakharov from Central Michigan University. Delve into the intricacies of metric graphs, divisors, and linear equivalence, while examining the Jacobian and Picard groups. Investigate the geometric interpretation of volume formulas and the structure of the tropical Abel-Jacobi map. Analyze double covers of graphs and metric graphs, and discover the discrete Prym for double covers of finite graphs. Gain insights into the construction of double covers, the volume of tropical Prym varieties, and the geometrization of volume formulas and Abel-Prym maps.