Theguidingprincipleinthisbookistousedifferentialformsasanaidinexploringsomeofthelessdigestibleaspectsofalgebraictopology.Accord-ingly，wemoveprimarilyintherealmofsmoothmanifoldsandusethedeRhamtheoryasaprototypeofallofcohomology.Forapplicationstohomotopytheorywealsodiscussbywayofanalogycohomoiogywitharbitrarycoefficients.Althoughwehaveinmindanaudiencewithpriorexposuretoalgebraicordifferentialtopology，forthemostpartagoodknowledgeoflinearalgebra，advancedcalculus，andpoint-settopologyshouldsuffice.Someacquaintancewithmanifolds，simplicialcomplexes，singularhomologyandcohomology，andhomotopygroupsishelpful，butnotreallynecessary.Withinthetextitselfwehavestatedwithcarethemoreadvancedresultsthatareneeded，sothatamathematicallymaturereaderwhoacceptsthesebackgroundmaterialsonfaithshouldbeabletoreadtheentirebookwiththeminimalprerequisites.