A general theory for rigidly rotating spiral waves including multi-armed ones is presented. This theory is valid over the entire spatial region including the core. It is also valid for both oscillating and excitable kinetics. The notions of winding number and generalized phase are introduced so that we may conveniently deal with the multi-armed waves. By employing a phase averaging procedure, some symmetry properties of the wave pattern are discussed, which is important in investigating the behaviour of the spiral waves near the core. We show a radically different behaviour for different number of arms. A simple model is investigated and simulated numerically to clarify some essential points of our theory.