This chapter introduces some fundamental results in survival analysis. We first describe what is censored failure time data and how to interpret the failure time distribution. Two nonparametric methods for estimating the survival curve, the life table estimator and the Kaplan-Meier estimator, are demonstrated. We then discuss the two-sample problem and the usage of the log-rank test for comparing survival distributions between groups. Lastly, we discuss in some detail the proportional hazards model, which is a semiparametric regression model specifically developed for censored data. All methods are illustrated with artificial or real data sets.