Linear potential sweep voltammetry in thin layers of solution offers numerous advantages for the study of irreversible reactions. The experimental equations, derived here for representative reaction types, are simpler than their counterparts in ordinary voltammetry, and may in some cases be solved directly for the electrochemical rate parameters, k0 and αn0. Rate measurements in thin layers do not require that both members of the reactant couple be present initially in solution. The physical and mathematical simplicity of thin layer voltammetry may allow the otherwise impossible study of irreversible systems involving multiple reactants, multiple charge-transfer steps or complicated stoichiometry. Experiments in which the theory is verified and exploited for studies of fundamental interest will be described in subsequent communications.