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Group Theory is the essential mathematical framework for understanding symmetry in molecules and materials. This course provides a rigorous, step-by-step introduction to foundational group theory concepts, enabling you to systematically identify symmetry elements, classify point groups, and utilize character tables for advanced problem-solving. What you'll learn: * Understand the fundamental definitions and axioms of abstract groups, subgroups, and classes. * Identify and apply all symmetry elements and operations found in two- and three-dimensional molecular systems. * Master the systematic approach for classifying molecules into Schoenflies point groups. * Learn to read, interpret, and utilize character tables to determine irreducible representations. * Apply group theory principles to analyze molecular vibrations and predict activity in IR and Raman spectroscopy. The course begins with key terminology and the abstract basis of group theory before moving into the practical identification of symmetry elements in molecules. We then focus on developing systematic methods for point group classification and applying character tables to solve real-world chemical problems. This course is designed for absolute beginners in group theory, particularly students or professionals preparing for rigorous theoretical examinations in chemistry or physics. No prior knowledge of abstract algebra is required. Start reading today and build a solid foundation in chemical symmetry.