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A general theory for the electromagnetic fields of dipoles in stratified isotropic media is outlined. The stratified model consists of a stack of layers sandwiched between two semi-infinite media. Either an electric or a magnetic dipole can be placed at any position in the stack, or in the upper or lower half-space. Dipoles can be electric or magnetic and can be oriented horizontally or vertically. The fields in the layer containing the source are given in terms of reflection coefficients, impedance and admittance terms, and wavenumber ratios. Recursion relations are developed to propagate the Hankel-domain field coefficients to other layers or to the half spaces. This allows the observation point to be placed anywhere except at the source. Numerical checks show that the derived algebra is at least self-consistent.