Gaussian mixture model occurs commonly in various scientific research. A mixture is a population that consists of components whose probability distributions could, but should not necessarily, belong to the same family of distributions. This thesis studies Gaussian mixtures whose number of components is finite and known in advance. For those mixtures, we constructed a model in a way that the distribution parameters were estimated and observations were assigned to the components. Parameter estimation methods that were used come both from frequentist and Bayesian statistics and are consolidated with the Expectation–Maximization algorithm (the EM algorithm). Each mixture model should be adjusted according to the available information on the population. The simplest case that is modelled is the one where densities of the components are known and only allocation of the observation remains. Allocation is conducted by using the naıve Bayes classifier. In the case where component densities are unknown and the allocation of the observations is known, only parameter estimation is required. Unknown parameters are estimated by using the method of maximum likelihood estimation along with the Bayesian method of estimation. The last studied case is the example of a population for which both the component parameters and the allocation is unknown. That problem is easily solved by using the EM algorithm which is in this thesis theoretically explained and implemented on the real–life population. The process of modelling Gaussian mixtures is illustrated on the population of three penguin species for which all the units are allocated to the components by using the EM algorithm. The model is given as a linear combination of multivariate normal distributions whose parameters were estimated.