The main objective of this thesis was to represent the mathematical aspects of the popularly known Rubik’s cube. Thereby we elaborated on group theory and analogously on combinatoric problems tied to Rubik’s cube. Using the fact that the set of all moves on a Rubik’s cube generates an algebraic structure of a group, certain structural properties are demonstrated such as associativity, identity, and invertibility, as well as two basic properties of invertibility which in the context of this thesis are called properties of opposite moves on the Rubik’s cube. Furthermore, by displaying effects of the conjugate and commutator on the Rubik’s cube as moves which have assigned cycles as a consequence, complex concepts from group theory are presented with an intuitive and reasonable approach. On the issue of combinatorics, the thesis touched upon the number of all possible combinations of the Rubik’s cube, as well as the minimum number of moves sufficient for solving a cube given an arbitrary position. In this case, a parameterized metric was used indirectly for observing moves on a Rubik’s cube, which demonstrated that defining a move on the Rubik’s cube as a turn of one of its sides by exactly 90 degrees is only one of the possible definitions of a move which generally depends on the selection of its metric (In this case, the selection is of the so-called quarter metric). In the last chapter, a review was given of the algebraic group which can be derived from the popular fifteen piece sliding puzzle game. The purpose of this review was of a comparative nature, and as such certain similarities are highlighted between the processes of solving the fifteen piece puzzle and Rubik’s cube.