Christophe Garban is a professor of mathematics at Université Lyon I, France. Jeffrey Steif is a Professor of Mathematical Sciences at Chalmers University of Technology, Gothenburg, Sweden.

• 1. Boolean functions and key concepts; 2. Percolation in a nutshell; 3. Sharp thresholds and the critical point; 4. Fourier analysis of Boolean functions; 5. Hypercontractivity and its applications; 6. First evidence of noise sensitivity of percolation; 7. Anomalous fluctuations; 8. Randomized algorithms and noise sensitivity; 9. The spectral sample; 10. Sharp noise sensitivity of percolation; 11. Applications to dynamical percolation; 12. For the connoisseur; 13. Further directions and open problems.

'Presented in an orderly, accessible manner, this book provides an excellent exposition of the general theory of noise sensitivity and its beautiful and deep manifestation in two dimensional critical percolation. The authors, both of whom are major contributors to the theory, have produced a very thoughtful work, bringing the intuition and motivations first. Noise sensitivity is a natural concept that recently found diverse applications, ranging from quantum computation and complexity theory to statistical physics and social choice. Two dimensional critical percolation is a striking and canonical random object. The book elegantly unfolds the story of integrating the general theory of noise sensitivity into a concrete study, allowing for a new understanding of the percolation process.' Itai Benjamini, Weizmann Institute of Science, Israel