Group-theoretic bifurcation theory presented in Chap. 8 is applied to systems with dihedral group symmetry. The perfect and imperfect bifurcation behaviors of such systems in the neighborhood of bifurcation points are investigated using bifurcation equations. A hierarchy of subgroups expressing recursive bifurcation is obtained. Chapter 7 gives fundamentals of group and group representation employed herein. This chapter is a prerequisite for Chaps. 10 – 13 that deal with perfect and imperfect bifurcations of such systems.