The continuous interest in the social network area contributes to the fast development of this field. The new possibilities of obtaining and storing data facilitate deeper analysis of the entire network, extracted social groups and single individuals as well. One of the most interesting research topic is the dynamics of social groups, it means analysis of group evolution over time. Having appropriate knowledge and methods for dynamic analysis, one may attempt to predict the future of the group, and then manage it properly in order to achieve or change this predicted future according to specific needs. Such ability would be a powerful tool in the hands of human resource managers, personnel recruitment, marketing, etc. The social group evolution consists of individual events and seven types of such changes have been identified in the paper: continuing, shrinking, growing, splitting, merging, dissolving and forming. To enable the analysis of group evolution a change indicator - inclusion measure was proposed. It has been used in a new method for exploring the evolution of social groups, called Group Evolution Discovery (GED). The experimental results of its use together with the comparison to two well-known algorithms in terms of accuracy, execution time, flexibility and ease of implementation are also described in the paper.