Explores the martingale approach to the statistical analysis of counting processes, with an emphasis on application of those methods to censored failure time data. Introduced in the 1970s, this approach has proven to be remarkably successful in yielding results about statistical methods for many problems arising in censored data. Offers a thorough treatment of both the calculus of martingales needed for the study of counting processes and of the most important applications of these methods to censored data. In addition, it examines classical problems in asymptotic distribution theory for counting process methods as well as some newer methods for graphical analysis and diagnostics of censored data. Exercises are included to provide students with practice in applying martingale methods and insight into the calculus itself.