This lecture is the second part of the Uhlenbeck Lecture Course on Tropical Geometry presented by Melody Chan from Brown University as part of the 2025 Program for Women+ and Mathematics at the Institute for Advanced Study. Explore tropical geometry as a modern degeneration technique in algebraic geometry, where families of algebraic varieties are associated with entirely combinatorial limiting objects. Discover the beautiful topics of tropical curves, tropical abelian varieties, and their moduli spaces through this comprehensive introduction. The lecture, scheduled for May 20, 2025, offers a deep dive into this fascinating field that serves as a drastic but powerful degeneration approach in modern algebraic geometry.