The field of large deviations deals with rare events in probability theory. It considers events whose probability tends to zero exponentially fast. In many cases, the exponential rate of decay can be identified precisely, and the rate function helps understanding the rare event itself. It shows the most likely way how the event is realized, and it can often be used for proving a law of large numbers. Thanks to these properties, large deviations are used, e.g., for Markov chains, statistical mechanics, SDEs, random walks in a random environment or extremal combinatorics. In this talk, I will introduce large deviations starting with the example of coin tosses, I will present Cramér's theorem and sketch some applications of large deviation theory.