Explore a comprehensive lecture on approximation algorithms in theoretical computer science. Delve into the intricacies of Boolean formula satisfiability, algorithmic complexity theory, and various optimization problems. Learn about Gavril's Approximation Algorithm, Max-Cut, and the Vertex-Cover problem, including examples and analyses of greedy approaches. Discover the 2-approximation theorem for Vertex-Cover and explore the k-Coverage and Pokémon-Coverage problems. Examine the Traveling Salesperson Problem (TSP) with practical examples, and gain insights into its applications in museum exhibit planning and textbook organization.