In this age of big data, the number of features measured on a person or object can be large and might be larger than the number of observations. This book shows how the sparsity assumption allows us to tackle these problems and extract useful and reproducible patterns from big datasets. The authors cover the lasso for linear regression, generalized penalties, numerical methods for optimization, statistical inference methods for fitted (lasso) models, sparse multivariate analysis, graphical models, compressed sensing, and much more.