Explore a groundbreaking lecture on the Connectivity Augmentation Problem (CAP) presented by Afrouz Jabal Ameli at the Hausdorff Center for Mathematics. Delve into the state-of-the-art research that breaches the long-standing 2-approximation barrier for CAP. Learn about the classification of links, incident links, and the innovative reduction to the Steiner Tree problem. Discover the lower bound techniques, approximation algorithms, and the novel marking scheme that led to this significant advancement. Examine the analysis of the approximation factor, grouping strategies, and recent advances in the field. Conclude with a discussion on open problems, providing insights into future research directions in graph connectivity augmentation.