In this paperwork we are introduced to mathematical modeling of motion using the tools of linear algebra. The emphasis is on the theoretical processing of tools and development of its understanding, despite the abstractness of the theoretical mathematics that can be challenging. Binary operations and algebraic structures are being defined togather with all their properties starting from the simplest ones to the more complicated ones. For the ease of understanding there are expamples and explanations for every term. We are also being introduced to the linear operators with their matrix representations. These representations are important because using the matrix multiplication we can in an elegant way describe the motion. In that sense, the rotation matrices are being developed which are used to describe the rotational motion together with the homogeneous matrices which can be used to describe the translations, but also the complex motion consisting of both rotation and translation. We have proved that rotation matrices form a group which is denoted with SO(n) and concluded that, analogous to that, homogeneous matrices form the SE(n) group. By combining the elements of these groups we can fully model the motion in three-dimensional space, since every motion can be described as the composition of rotations and translations. At the end of this paperwork there is a practical example from robotics where we solve the inverse kinematics problem and explain the usage of the linear operators and groups.