Explore the foundations of geometric group theory in this comprehensive lecture on Property(T), median spaces, and CAT(0) cubical complexes. Delve into the first part of Indira Chatterji's minicourse, presented as part of the "Geometry in Groups" program at the International Centre for Theoretical Sciences. Gain insights into these fundamental concepts and their applications in the rapidly evolving field of geometric group theory. Learn from an eminent researcher known for her expository skills and contribute to the growing research network in this dynamic area of mathematics.