The microscopic processes of an electron avalanche are discussed and calculations are made by the statistics of collision probability.Two important quantities

the order of collision and the electron generation

are introduced to clarify the mechanism.The rigorous formula for the electron avalanche as deduced from the concept of "electron generation" is in a form of a polynomial with finite terms

but not an exponential function as ordinarily recognized.Theoretically

the electron avalanche discharge can be classified into two natural types: the strict avalanche discharge and the quasi-avalanche discharge. An explanation of the existence of the avalanche discharge under vacuum is given.