Thepurposeofthisbookistoprovideanintroductiontotheapplicationsofquantumfieldtheoreticmethodstosystemsoutofequilibrium.Thereasonforaddingabookonthesubjectofquantumfieldtheoryistwo-fold：thepresentationis，tomyknowledge，thefirsttoextensivelypresentandapplytonon-equilibriumphenomenathereal-timeapproachoriginallydevelopedbySchwinger，andsubsequentlyappliedbyKeldyshandotherstoderivetransportequations.Secondly，theaimistoshowtheuniversalityofthemethodbyapplyingittoabroadrangeofphenomena.Thebookshouldthusnotjustbeofinteresttocondensedmatterphysicists，buttophysicistsingeneralasthemethodisofgeneralinterestwithapplicationsrangingthewholescalefromhigh-energytosoftcondensedmatterphysics.Theuniversalityofthemethod，astestifiedbytherangeoftopicscovered，revealsthatthelanguageofquantumfieldsistheuniversaldescriptionoffluctuations，betheyofquantumnature，thermalorclassicalstochastic.Thebookisthusintendedasacontributiontounifyingthelanguagesusedinseparatefieldsofphysics，providingauniversaltoolfordescribingnon-equilibriumstates.