In the previous chapter we used the idea that a symmetry of a geometric object like a triangle or tetrahedron must take vertices to vertices. For example, specifying where the vertices of a tetrahedron are sent completely determines the symmetry function. We used this reasoning to determine a complete list of symmetries of the tetrahedron. We called a specification of how the vertices are moved a permutation of the vertices. We found that using permutation notation was one way to compute the composition of symmetries of the tetrahedron (or some other geometric figure). We will now consider the notion of permutations in an abstract setting. This will provide us with a great source for examples and computational techniques when we move to abstract groups in the next chapter.