The known integral representation of electromagnetic fields is reviewed. Based on the review, a new formulation allows us to model any general case. The formulation of PEC, dielectric, dielectric with metallic surfaces, and dielectric scatterers with dielectric or PEC inclusions is derived. Finally, a new operator notation allows a concise and accurate representation of the integral equation formulations. The electric field integral equation and the magnetic field integral equation are contained in this formulation.