Mazes have a long history and there are a lot of other mathematical aspects beside the logical reasoning needed for generating and solving them. In this thesis a clear and comprehensive overview of these aspects is presents, understandable to a wide range of readers of various ages and mathematical backgrounds. A brief history of mazes is presented in the opening part, as are basic notions of graph theory needed for understanding of presented algorithms. The main part of the thesis are maze generation algorithms and maze solving algorithms, which are described in detail. Algorithms are described in pseudocode and the reader can follow the steps to demonstrate generating or solving a maze with a pen and paper. Readers with a sufficient level of computer knowledge could implement the pseudocodes in a computer language of their choice and use them to generate or solve mazes. The thesis is supplemented with examples of how to use mazes in popularization if mathematics. The examples can be used in teaching as well, and one of the examples was particularly designed and conducted in the course Methodical practice of mathematics in elementary school.