The main subject studied in this dissertation is a multi-layered social network (MSN) and its analysis. One of the crucial problems in multi-layered social network analysis is community extraction. To cope with this problem the CLECC measure (Cross Layered Edge Clustering Coefficient) was proposed in the thesis. It is an edge measure which expresses how much the neighbors of two given users are similar each other. Based on this measure the CLECC algorithm for community extraction in the multi-layered social networks was designed. The algorithm was tested on the real single-layered social networks (SSN) and multi-layered social networks (MSN), as well as on benchmark networks from GN Benchmark (SSN), LFR Benchmark (SSN) and mLFR Benchmark (MSN) a special extension of LFR Benchmark, designed as a part of this thesis, which is able to produce multi-layered benchmark networks. The second research problem considered in the thesis was group evolution discovery. Studies on this problem have led to the development of the inclusion measure and the Group Evolution Discovery (GED) method, which is designed to identify events between two groups in successive time frames in the social network. The method was tested on a real social network and compared with two well-known algorithms regarding accuracy, execution time, flexibility and ease of implementation. Finally, a new approach to prediction of group evolution in the social network was developed. The new approach involves usage of the outputs of the GED method. It is shown, that using even a simple sequence, which consists of several preceding groups sizes and events, as an input for the classifier, the learned model can produce very good results also for simple classifiers.