Quantile regression is gradually emerging as a unified statistical methodology for estimating models of conditional quantile functions. This monograph is the first comprehensive treatment of the subject, encompassing models that are linear and nonlinear, parametric and nonparametric. Roger Koenker has devoted more than 25 years of research to the topic. The methods in his analysis are illustrated with a variety of applications from economics, biology, ecology and finance and will target audiences in econometrics, statistics, and applied mathematics in addition to the disciplines cited above. Author resource page: http: //www.econ.uiuc.edu/ roger/research/rq/rq.html Roger Koenker is the winner of the 2010 Emanuel and Carol Parzen Prize for Statistical Innovation, awarded by the the Department of Statistics at Texas A&M University.