This final chapter provides some applications of Wigner’s theorem and its generalizations described in Chapter 4. The first is classical Kadison’s theorem concerning automorphisms of the convex set of all bounded positive operators of trace one. In the second section, we consider the real vector space formed by all self-adjoint operators of finite rank and investigate linear transformations sending projections of fixed rank $k$ to projections of rank $k$ as well as linear transformations which map projections of a fixed rank to projections of other fixed rank.