Extreme value theory is a branch of stochastics that deals with the maxima and minima of random variables, records and extremely rare events. Maxima and minima of random variables play an important role in many areas: think for example of extreme weather events, extreme events in actuarial mathematics or records in sports. The following topics are expected to be covered in this lecture:

• Maxima and minima of independent and identically distributed random variables.
• Max-stable distributions and their domain of attraction.
• Regular variation.
• Order statistics.
• Records and the extreme value process.
• Point processes and convergence of the extreme values to the point processes.
• Statistics of extreme values.
• Multivariate extreme value theory.

You can download the lecture notes from Learnweb.
You can find more scripts for similar lectures online:

Script by Prof. Dr. Matthias Löwe: Link

Script by Prof. Dr. Anton Bovier: Link

• Paul Embrechts, Claudia Klüppelberg, Thomas Mikosch. Modelling Extremal Events for Insurance and Finance. Springer, 1997 
• Laurens de Haan, Ana Ferreira. Extreme Value Theory: An Introduction. Springer, 2006
• Sidney Resnick. Heavy-Tail Phenomena: probabilistic and statistical modeling. Springer, 2007.
• Sidney Resnick. Extreme Values, Regular Variation and Point Processes. Springer, 2007 

• Michael Falk, Jürg Hüsler, Rolf-Dieter Reiss. Laws of Small Numbers: Extremes and Rare Events. Birkhäuser. 

• E. J. Gumbel. Statistics of Extremes. Dover Publishers.