Fundamentals of group-theoretic bifurcation theory are introduced as a mathematical methodology to deal with agglomeration in economic geography, which is captured in this book as bifurcation phenomena of systems with dihedral or hexagonal symmetry. The framework of group-theoretic bifurcation analysis of economic agglomeration is illustrated for the two-place economy in new economic geography. Symmetry of a system is described by means of a group, and group representation is introduced as the main tool used to formulate the symmetry of the equilibrium equation of symmetric systems. Group-theoretic bifurcation analysis procedure under group symmetry is presented with particular emphasis on Liapunov–Schmidt reduction under symmetry. Bifurcation equation, equivariant branching lemma, and block-diagonalization are introduced as mathematical tools used to tackle bifurcation of a symmetric system in Chaps. 3– 9.