The prime objective of this thesis is to give an introduction into the statistical theory that is crucial for understanding extreme value modelling via block maxima method, as well as to try and illustrate the use of said block maxima method on real-life data. At first, it is described how to represent the available data as a sequence of independent, identically distributed random variables and how block maxima are actually found. The main objective of block maxima method consists of determining the distribution of block maxima, which can sometimes be achieved by applying Fisher-Tippett-Gnedenko theorem. Fisher-Tippett-Gnedenko theorem, along with its proof, represents the central theoretical result of this thesis. The importance of Fisher-Tippet-Gnedenko theorem lies in the fact that it provides all distribution families that can appear as limits for the block maxima distributions, regardless of the distribution of the initial data. Said distribution families are widely known as Gumbel, Frechet and Weibull families. This thesis also contains a brief review of maximum domains of attraction of Gumbel’s, Frechet’s and Weibull’s distributions, along with examples of some famous distribution functions that belong to one of said maximum domains of attraction. Next, GEV family is introduced as an unification of Gumbel’s, Frechet’s and Weibull’s family and a description is given on how to adapt the right GEV model to the available data. The key to estimating model parameters, as well as to determining the confidence of obtained estimates, surely was maximum likelihood estimation with its asymptotic properties. Moreover, the terms return level and return period are proposed as fundamental in understanding the extrapolated extreme values. Return level denotes a value that might be exceeded in any particular block with probability p, which corresponds to the reciprocal value of the observed return period. The application of block maxima method is illustrated with the analysis of three real-life datasets: the first one contains data about annual maximum sea-levels, the second dataset consists of measurements of glass fiber breaking strengths, and the third one includes measurements of maximum daily temperatures in Zagreb, Croatia. At last, this thesis also contains a short overview of classical statistical results that are crucial for understanding the presented extreme value theory results.