The analysis of failure times is an important field in statistical research with applications in various areas, including manufacturing, demography, econometrics and epidemiology. There are many publications which deal with the analysis of failures in continuous time. However, failure times are often discrete in practice. This book presents statistical methods for the analysis of discrete failure times. It aims to introduce readers to basic and advanced concepts of discrete hazard modelling, to demonstrate the relationship between generalised linear models and hazard models and to consider applications from the social sciences, economics and biomedical sciences. The book also provides functions to apply the statistical methodology presented in the statistical software R.