Explore the intricacies of Hardness of Approximation in this third installment of Ryan O'Donnell's tutorial series, recorded at the Metric 2011 workshop at IHP. Delve into advanced topics such as IntroMax 3 Lin, Max 3 Lin instances, variables, optimal solutions, and notation. Gain insights into Fourier analysis, examining suggestive F-formulas, edge weights, and Fourier coefficients. Investigate the concepts of G3 and G4, and understand the implications of empty suggestion sets. Originally captured by Nicolas Schabanel, this hour-long lecture offers a comprehensive exploration of complex approximation algorithms and their applications in computational theory.