  Antiferromagnetism and superconductivity are both fundamental and common
states of matter. In many strongly correlated systems, including the high Tc
cuprates, the heavy fermion compounds and the organic superconductors, they
occur next to each other in the phase diagram and influence each other's
physical properties. The SO(5) theory unifies these two basic states of matter
by a symmetry principle and describes their rich phenomenology through a single
low energy effective model. In this paper, we review the framework of the SO(5)
theory, and its detailed comparison with numerical and experimental results.
