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It is shown that most of the energy deposited by fast charged particles traversing matter occurs through ionization, i.e., the ejection of electrons during the atomic collision. The important mechanisms of ionization are identified and several methods of calculating the relevant differential and total cross sections are described. These include both classical and quantum theoretical methods and two semi-empirical models. The calculational methods were intended only for light, bare-ion projectiles, and care must be exercised in extending them to heavy, dressed projectiles.