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Time-to-event data are ubiquitous in fields such as medicine, biology, demography, sociology, economics and reliability theory. Recently, a need to analyze more complex event histories has emerged. Examples are individuals that move among several states, frailty that makes some units fail before others, internal time-dependent covariates, and the estimation of causal effects from observational data.The aim of this book is to bridge the gap between standard textbook models and a range of models where the dynamic structure of the data manifests itself fully. The common denominator of such models is stochastic processes. The authors show how counting processes, martingales, and stochastic integrals fit very nicely with censored data. Beginning with standard analyses such as Kaplan-Meier plots and Cox regression, the presentation progresses to the additive hazard model and recurrent event data. Stochastic processes are also used as natural models for individual frailty; they allow