Survival analysis is interested in nonnegative random variables and their characteristics such as survival function, probability density, hazard rate and regression. Nonparametric curve estimation allows one to analyze data and to estimate the above-mentioned characteristics without assuming the shape of an estimated curve. This chapter reviews basics of probability, mathematical statistics and nonparametric curve estimation for directly observed random variables, and presents discussion of typical data modifications in survival analysis. Section 1.1 is a brief probability review of random variables and their main characteristics. Section 1.2 is a review of nonparametric curve estimation. In particular, it presents results on orthogonal series approximation and the E-estimation algorithm used throughout the book. Installation of the book’s R package and a short tutorial on its use can be found in Sect. 1.3. Exercises in Sect. 1.4 will allow the reader to review basics of probability and statistics. Section 1.5, called the Notes, presents historical and bibliographical remarks.