This lecture is the second part of Ken'ichi Ohshika's presentation on Thurston's Asymmetric Metric on Teichmüller Space, delivered as part of the "New Trends in Teichmüller Theory" program at the International Centre for Theoretical Sciences. Explore advanced concepts in the metric theory of Teichmüller spaces, focusing on Thurston's asymmetric metric and its implications. The program brings together various mathematical disciplines including complex analysis, hyperbolic geometry, dynamics, partial differential equations, and geometric group theory to examine cutting-edge developments in Teichmüller theory. Designed for researchers, postdoctoral fellows, and graduate students interested in the intersection of these mathematical fields, this 81-minute lecture contributes to a two-week thematic program that aims to foster collaboration and research initiatives in this evolving area of mathematics.