An effective-mass theory of the properties of excitons in isolated GaAs/${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$As quantum wells is presented. The phenomenon of exciton mixing induced by the complicated valence-band structure is emphasized. The effects of external perturbations such as electric and magnetic fields and uniaxial pressure normal to quantum wells grown in different crystal directions are calculated. Exciton mixing is found to cause many observable effects on transition energies and oscillator strengths.