The Townsend equation for the passage of a spark is analyzed and its inadequacy for explaining sparks in air at near atmospheric pressures is demonstrated. The mechanisms active in air at higher pressures,viz., the electron avalanche and its tip field, photo‐ionization in the gas and positive streamer formation are presented. A quantitative criterion for streamer formation is applied to give a quantitative theory for spark breakdown in air at atmospheric pressures. The theory gives quantitative agreement with experiment and predicts departures from Paschen's law. At values of the product, pressure times gap length less than 200 mm×cm in air, the new mechanism is unimportant. The theory is applied to longer sparks at atmospheric pressures and the effect of the decrease in density of photo‐ionization in longer avalanches considered. This leads to a modification of the Meek mechanism by which the electron avalanche slows down while a retrograde positive streamer moves at high speed to the cathode and then advances again. This mechanism enables one to discuss the breakdown potentials of unsymmetrical gaps showing the difference in sparking potential between positive and negative points. The mechanism is correlated with the passage of lightning discharges. Alterations of Meek's theory of the stepped leader are indicated. Part I describes the classical theory of spark discharge and the nature of the mechanism which must be active at higher pressures. Part II will consider streamer formation and spark breakdown in short and long gaps.