For the description of an assembly of two-level atoms, atomic coherent states can be defined which have properties analogous to those of the field coherent states. The analogy is not fortuitous, but is shown to be related to the group contraction of exponential operators based on the angular momentum algebra to exponential operators based on the harmonic-oscillator algebra. The derivation of the properties of the atomic coherent states is made easier by the use of a powerful disentangling theorem for exponential angular momentum operators. A complete labeling of the atomic states is developed and many of their properties are studied. In particular it is shown that the atomic coherent states are the quantum analogs of classical dipoles, and that they can be produced by classical fields.