Myintentionisthatthisbookserveasareferenceworkoninteractingparticlesystems，andthatitbeusedasthebasisforanadvancedgraduatecourseonthissubject.Thebookshouldbeofinterestnotonlytomathematicians，butalsotoworkersinrelatedareassuchasmathematicalphysicsandmathematicalbiology.Theprerequisitesforreadingitaresolidone-yeargraduatecoursesinanalysisandprobabilitytheory，atthelevelofRoyden（1968）andChung（1974），respectively.Materialwhichisusuallycoveredinthesecourseswillbeusedwithoutcomment.Inaddition，afamiliaritywithanumberofothertypesofstochasticprocesseswillbehelpful.However，referenceswillbegivenwhenresultsfromspecializedpartsofprobabilitytheoryareused.Noparticularknowledgeofstatisticalmechanicsormathematicalbiologyisassumed.Whilethisisthefirstbook-lengthtreatmentofthesubjectofinteractingparticlesystems，anumberofsurveysofpartsofthefieldhaveappearedinrecentyears.AmongtheseareSpitzer（1974a），Holley（1974a），Sullivan（1975b），Liggett（1977b），Stroock（1978），Griffeath（1979a，1981），andDurrett（1981）.Thesecanserveasusefulcomolementstotheoresentwork.