In simple survival analysis, where only one failure event is studied, there is a simple relationship between the hazard function for the occurrence of the event and the probability of no event occurring in an interval (the survival function). However, when competing risks are present the situation is more complex and the survival function depends on the hazard function for all the competing events. We will study situations where competing risks are present with examples taken primarily from medicine and public health, the generic medical example being death from different causes. The basic oncepts of cause-specific hazards and cumulative incidence functions will be defined and statistical inference for these parameters will be discussed. Both non-parametric inference, models based on piecewise constant hazards, and regression analysis will be covered.