In this thesis, we dealt with low-rank approximation of matrices and well known algorithms for such purpose. The basis for these algorithms is singular value decomposition (SVD). The main topic of this thesis is an overview of hierarchical matrices (HODLR, \(\mathcal{H}\), HSS, \(\mathcal{H}^2\)) and operations on them. It has been shown that under certain conditions, such as a small (numerical) rank of off-diagonal matrix blocks, matrices can be stored in less than \(O(n^2) \) storage complexity and matrix operations are executed in almost linear time. This is especially useful for matrices of large dimension, such as those that are most often encountered in practice. The greatest emphasis was put on HODLR matrices because we implemented them in the Python programming language. At the end of the thesis, a number of examples of matrices that can be well stored in HODLR structure and an overview of the most important applications of hierarchical matrix formats is given.