Explore the foundations of Fourier analysis for Boolean functions in this graduate-level lecture from Carnegie Mellon University's "CS Theory Toolkit" course. Delve into the Fourier transform of real-valued Boolean functions, covering key concepts such as basic Boolean functions, polynomials, and Fourier coefficients. Learn from Professor Ryan O'Donnell's expertise, drawing from his book "Analysis of Boolean Functions." Gain essential mathematical and computer science fundamentals crucial for research in theoretical computer science over the course of this 32-minute video lecture.