This chapter provides a comprehensive introduction to the fundamental concepts of survival analysis, focusing on the role of censoring and the mathematical functions that characterize survival time distributions. Survival analysis is widely applied in medical research, engineering, social sciences, and demography, where the primary interest lies in analyzing time-to-event data. A key feature of such data is censoring, which occurs when the event of interest is not fully observed for all individuals within the study period. The chapter presents a detailed classification of censoring types, including Type I, Type II, Type III, random, left, right, and interval censoring, along with the distinction between censoring and truncation. The mathematical framework of survival analysis is also discussed through essential survival time functions such as the survival function, probability density function, hazard function, cumulative hazard function, and mean residual life function. These functions are foundational for understanding the distribution and risk associated with event times. This chapter aims to equip readers with a clear conceptual and mathematical understanding of the basic tools and issues in survival analysis, serving as a necessary starting point for more advanced modeling and inference techniques in censored data analysis.