The theory of the rubidium-87 maser is described. It is shown that the maser power output is a critical function of the rubidium density, light intensity, and cavity $Q$. Fundamental parameters and constants of the maser are grouped together to define an oscillation parameter ${{\ensuremath{\Gamma}}_{m}}^{\ensuremath{'}}$ which determines the oscillation characteristics of the maser. Spin-exchange calculations in rubidium are presented. The relaxation times ${T}_{1}$ and ${T}_{2}$ due to spin-exchange interactions are related to each other, and it is shown that ${T}_{2}=(\frac{8}{5}){T}_{1}$. A method of determining the spin-exchange cross section in terms of fundamental constants and maser parameters is described. Results of experiments made to verify these calculations are given. It is found in general that the results agree with the theory, but slight discrepancies exist. Tentative explanations are given.