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There are many books covering survival data, that is data covering the time to some event. In the standard case, the event is death, but the topic is much broader. This book, however, covers the extension to multivariate survival data. In popular terms, this means everything where more than one time is involved. One such type is the survival times of several individuals, which are related in some way, and where independence cannot be assumed. Another type of data is the multiple data, where we study repeated occurrences of the same event. A further type is the times to several events for the same persons, like outbreak of disease, time to complication and death. Such types of data are only briefly covered by other books. Most of the material in this book is only available in journal papers, some of it is not available in writing at all.