Extreme value statistics (EVS) and the statistics of records in a random sequence are truly interdisciplinary topics, spanning statistics and mathematics on one side to the physics of disordered systems on the other. They have important practical applications in a wide variety of fields, such as climate science, finance, spin-glasses, random matrices. One of the basic questions in EVS is how the maximum or minimum of a time series fluctuates from one sample to another. This is well understood when the time series entries are independent and identically distributed (IID), which is the subject of the classical theory of EVS. However, more recently, EVS started to play a very important role in statistical physics. It turns out that in many physical systems the entries of the underlying time series are actually strongly correlated and the classical theory is no longer applicable, which has led to a plethora of activities in the statistical physics and mathematics communities. What is currently missing is a pedagogical book with examples illustrating the basic tools and techniques. The purpose of this book is to provide an introductory monograph on this subject with a style adapted for a graduate student who only has a basic knowledge of probability theory and statistical mechanics. We present the basic ideas and tools using two simple models of time series: an IID sequence, where there is no correlation between the entries, and a random walk sequence, where the entries are strongly correlated. The EVS and related observables can be computed exactly for both models, as we illustrate with several examples and exercises.
