The thesis "Symmetries, Mathematics, and Algorithms of the Rubik's Cube" explores the complexity and mathematical aspects associated with the Rubik's Cube, starting with an introduction to basic concepts of symmetry. The thesis provides a detailed analysis of the groups and symmetries characterizing the structure of the cube and introduces fundamental concepts of group theory necessary for understanding this analysis. The historical context of the invention of the Rubik's Cube and its mechanism are also covered to provide a comprehensive overview. The main part of the thesis is dedicated to the mathematics and algorithms used for solving the Rubik's Cube. Key mathematical concepts such as permutations, parity, subgroups, Cayley graph, commutator, and conjugation are discussed. The beginner's algorithm for solving the cube is thoroughly explained through seven steps, including: Solving the first layer (edges and corners), Solving the second layer (F2L - First Two Layers), Forming the yellow cross, Swapping the side center pieces with yellow edges, Placing the yellow pieces in their correct positions, Orienting the last layer of the Rubik's Cube. This thesis demonstrates how mathematical principles and algorithms can optimize the process of solving the Rubik's Cube, providing deeper insight into its structure and complexity. The importance of mathematics in understanding and solving the Rubik's Cube is highlighted, offering an overview of possible directions for further research and the application of mathematical principles in similar puzzles.