Isometry is not only widely used to describe the motion of rigid bodies that is a mixture of rotational and translational motions of solids but is also an important tool in theoretical physics and geometry. The properties of isometry have been actively researched for a long time, and this theory is widely used in fields such as natural science, computer engineering, radiology, imaging science, and design. In this chapter, we will examine in detail the Aleksandrov problem, one of the ways to find necessary and sufficient conditions for characterizing the isometries defined between Euclidean spaces.