Flow of ions through voltage gatedchannels can be represented theoretically using stochastic differentialequations where the gating mechanism is represented by a Markov model. The flow through achannel can be manipulated using various drugs, and the effect of a given drugcan be reflected bychanging the Markov model. These lecture notes provide an accessibleintroduction to the mathematical methods needed to deal with these models. They emphasize the use ofnumerical methods and provide sufficient details for the reader to implementthe models and thereby study the effect of various drugs.  Examples in thetext include stochastic calcium release from internal storage systems in cells,as well as stochasticmodels of the transmembrane potential. Well known Markov models are studied anda systematic approach toincluding the effect of mutations is presented. Lastly, the book shows how to derive the optimal propertiesof a theoretical model of a drug for a given mutation defined in termsof a Markov model.