General Resources

• Some topics in the Analysis of Boolean functions, Ryan O'Donnell
  A brief introduction to Fourier Analysis on the Boolean Cube, Ronald de Wolf
  Inapproximability of NP-complete problems, discrete Fourier analysis, and geometry, Subhash Khot
  Social choice, computational complexity, Gaussian geometry, and Boolean functions, Ryan O'Donnell
  Program in Real analysis in Computer Science, Simons Institute
  Scribe notes for a course at UC Berkeley, taught by Elchanan Mossel
  Scribe notes for a course at UW Seattle, taught by Nati Linial
  Scribe notes for a course at Hebrew University, taught by Irit Dinur and Ehud Friedgut
  Scribe notes for a course at CMU, taught by Ryan O'Donnell
  Scribe notes for a course at UW Madison, taught by Dieter van Melkebeek
  Scribe notes for a course at Weizmann, taught by Guy Kindler
  Lecture notes for a course at Cambridge, taught by Tom Sanders
  Videos of a course at CMU, taught by Ryan O'Donnell
  Scribe notes for a ten-lecture minicourse, taught by Ryan O'Donnell
  Lecture notes for a course at NYU, taught by Oded Regev
  Lecture notes for a course at McGill, taught by Hamed Hatami
  Lecture notes for a course at the Technion, taught by Yuval Filmus
  Lecture notes for a course at UCSD, taught by Shachar Lovett
  Analysis of Boolean functions: advances and challenges, video of a talk by Gil Kalai
  Open problems in Analysis of Boolean Functions, Ryan O'Donnell
  Real Analysis in Computer Science: A collection of open problems, Simons Institute

References and supplementary reading material

• Lectures on Influence, sensitivity, and noise stability
  Collective coin flipping, robust voting schemes and minima of Banzhaf values, Michael Ben-Or and Nathan Linial
  Noise sensitivity of Boolean functions with applications to percolation, Itai Benjamini, Gil Kalai, Oded Schramm
  Computational applications of noise sensitivity, Ryan O'Donnell
  Tight bounds on the average sensitivity of k-CNF, Kazuyuki Amano
  Nati's influence, blogpost by Gil Kalai
  
• Lectures on Halfspaces
  On the characterization of threshold functions, Chao-Kong Chow
  The noise stability of weighted majority, Yuval Peres
  The Chow parameters problem, Ryan O'Donnell and Rocco Servedio
  Learning intersections and thresholds of halfspaces, Adam Klivans, Ryan O'Donnell, Rocco Servedio
  Spectral properties of threshold functions, Craig Gotsman and Nathan Linial
  The correct exponent for the Gotsman-Linial conjecture, Daniel Kane
  The average sensitivity of an intersection of halfspaces, Daniel Kane
  Slicing the hypercube, Michael Saks
  
• Lectures on Decision trees and query complexity
  Every decision tree has an influential variable, Ryan O'Donnell, Michael Saks, Oded Schramm, Rocco Servedio
  Decision trees and influence: an inductive proof of the OSSS inequality, Homin Lee
  The influence lower bound via query elimination, Rahul Jain and Shengyu Zhang
  Learning monotone decision trees in polynomial time, Ryan O'Donnell and Rocco Servedio
  Boolean decision trees: Problems and results, old and new, Michael Saks
  The need for structure in quantum speedups, Scott Aaronson and Andris Ambainis
  
• Lectures on Boolean circuits
  Computational limitations for small-depth circuits, Johan Håstad
  The average sensitivity of bounded-depth circuits, Ravi Boppana
  Constant depth circuits, Fourier transform, and learnability, Nathan Linial, Yishay Mansour, Noam Nisan
  An O(n^{loglog n}) learning algorithm for DNF under the uniform distribution, Yishay Mansour
  A switching lemma primer, Paul Beame
  The switching lemma, lecture notes by Ryan O'Donnell
  The switching lemma, blogpost by Parikshit Gopalan
  Tight bounds on the Fourier spectrum of AC⁰, Avishay Tal
  The entropy-influence conjecture, blogpost by Gil Kalai
• Lectures on Hardness amplification
  Hard-core distributions for somewhat hard problems, Russell Impagliazzo
  On Yao's XOR lemma, Oded Goldreich, Noam Nisan, and Avi Wigderson
  Hardness amplification within NP, Ryan O'Donnell
  Boosting and hard-core set construction, Adam Klivans and Rocco Servedio
  The Impagliazzo hard-core set theorem, blogpost by Luca Trevisan
• Lectures on Learning under the uniform distribution
  A hard-core predicate for all one-way functions, Oded Goldreich and Leonid Levin
  Learning decision trees using the Fourier spectrum, Eyal Kushilevitz and Yishay Mansour
  Learning functions of k relevant variables, Elchanan Mossel, Ryan O'Donnell, Rocco Servedio
  Finding correlations in subquadratic time, with applications to learning parities and the closest pair problem, Gregory Valiant
  Agnostically learning halfspaces, Adam Kalai, Adam Klivans, Yishay Mansour, Rocco Servedio
  Agnostically learning decision trees, Parikshit Gopalan, Adam Kalai, Adam Klivans
  Learning Boolean functions under the uniform distribution via the Fourier transform, Johannes Köbler and Wolfgang Lindner
  The junta problem, blogpost by Dick Lipton and Ken Regan
  Learning juntas, blogpost by Parikshit Gopalan
  
• Lectures on Property testing
  Self-testing/correcting with applications to numerical problems, Manuel Blum, Michael Luby, Ronitt Rubinfeld
  Linearity testing in characteristic two, Mihir Bellare, David Coppersmith, Johan Håstad, Marcos Kiwi, Madhu Sudan
  Testing juntas nearly optimally, Eric Blais
  Sublinear algorithms in learning and testing, scribe notes for a course taught by Rocco Servedio
  The art of uninformed decisions: A primer to property testing, Eldar Fischer
  Testing properties of Boolean functions, Eric Blais
  
• Lectures on Hypercontractivity
  Étude des coefficients Fourier des fonctions de L^p(G), Aline Bonami
  The influence of variables on Boolean functions, Jeff Kahn, Gil Kalai, Nathan Linial
  On Russo's approximate zero-one law, Michel Talagrand
  Boolean functions with low average sensitivity depend on few coordinates, Ehud Friedgut
  Hypercontractivity and its applications, Punyashloka Biswal
• Lectures on Limit theorems and Gaussian analysis
  Geometric bounds on the Ornstein-Uhlenbeck velocity process, Christer Borell
  Optimal inapproximability results for MAX‐CUT and other 2‐variable CSPs?, Subhash Khot, Guy Kindler, Elchanan Mossel, Ryan O'Donnell
  Noise stability of functions with low influences: Invariance and optimality, Elchanan Mossel, Ryan O'Donnell, Krzysztof Oleszkiewicz
  Gaussian noise sensitivity and Fourier tails, Guy Kindler, Naomi Kirshner, Ryan O'Donnell
  The central limit theorem, lecture notes by Terence Tao
  Invariance principles in theoretical computer science, video of a talk by Ryan O'Donnell
  Computational applications of invariance principles, Raghu Meka
  Alan Turing and the central limit theorem, Sandy Zabell