Graph partitioning is an optimization problem which can be used to solve many real-world problems, such as transportation network optimization, image segmentation and social networks analysis. This thesis focuses on partitioning of weighted graphs with equally weighted vertices. The key notions of graph matching, cut function, external and internal cut and balance of a partition are defined and explained. Graph partitioning problems are typically NP-hard, therefore, in order to solve them one needs to use heuristic and approximation algorithms. In this thesis several such algorithms are described, namely spectral partitioning algorithm and multilevel method. For the multilevel method, we describe algorithms for iterative coarsening of the graph, as well as algorithms for refining the partition obtained at the lower level to the higher level. Some of the well-known bipartitioning algorithms can be found there, such as the Kernighan-Lin algorithm and its improvement, the Fiduccia-Mattheyses algorithm. Solving techniques are described both from constrained and unconstrained partitioning point of view. In the final chapter an implementation for some of the mentioned algorithm is described. Their performance is compared on fully connected weighted graphs with vertices of equal weight.