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Learn about the fundamental concepts of discrete groups in this introductory lecture from the Fields Institute's Shared Graduate Courses Program, delivered by Professor Nikolay Bogachev from the University of Toronto. Explore the intersection of geometry, arithmetic, and dynamics as they relate to discrete groups during this hour-long session that kicks off a comprehensive graduate-level course. Gain foundational knowledge essential for understanding the mathematical principles that govern discrete group theory and its applications across multiple mathematical domains.