GaloisTheory,thetheoryofpolynomialequationsandtheirsolutions,isoneofthemostfascinatingandbeautifulsubjectsofpuremathematics.Usinggrouptheoryandfieldtheory,itprovidesacompleteanswertotheproblemofthesolubilityofpolynomialequationsbyradicals:thatis,determiningwhenandhowapolynomialequationcanbesolvedbyrepeatedlyextractingrootsusingelementaryalgebraicoperations.ThistextbookcontainsafullydetailedaccountofGaloisTheoryandthealgebrathatitneedsandissuitablebothforthosefollowingacourseoflecturesandtheindependentreader(whoisassumedtohavenopreviousknowledgeofGaloisTheory).Thesecondeditionhasbeensignificantlyrevisedandre-ordered;thefirstpartdevelopsthebasicalgebrathatisneeded,andthesecondacomprehensiveaccountofGaloisTheory.Thereareapplicationstoruler-and-compassconstructions,andtothesolutionofclassicalmathematicalproblemsofancienttimes.Therearenewexercisesthroughout,andcarefully-selectedexampleswillhelpthereaderdevelopaclearunderstandingofthemathematicaltheory.
