Thissssentiallyookningularomologyndohomologyithspecialmphasisnroductsndanifolds.toesotreatomotopytheoryxceptoromeasicotions,omexamples,ndomepplica-tionsfomologyoomotopy.oroestealitheneral（ised）homology,utanyormulationsndrgumentsningularomologyareohosenhatheylsopplyoeneralomology.ecausefheseabsencesavelsomittedpectralequences,heirainpplicationsinopologyeingoomotopyndeneralomologyheory.ch-cohomologysreatednimpledocashionorocallyompactsubsetsfanifolds;hortystematicreatmentorrbitrarypaces,emphasizingheniversalropertyfheech-procedure,sontainedinnppendix.Theookrewutfne-year\'soursenlgebraicopology,ndtcanervesextoruchourse.orhorterasicourse,ayfhalfear,neightsehapters（§1-4）,（§I-5,,）,Ⅵ（§,,,1,2）.srerequisiteshetudenthouldnowheelementaryartsfeneralopology,belianroupheory,ndhelanguagefategories-althoughurhapterprovidesittleelpwithheatterwo.oredagogicaleasons,avereatedntegralhomologynlypohapterfeaderreacherrefersohaveeneraloefficientsromheeginningeeedsoakenlyinoradaptions.Asoheutlayfheook,herereighthapters,-Ⅷandappendix,;achfhesesubdividedntoeveral.

Chapterreliminariesnategories,Abelianroups,ndomotopy1ategoriesndunctors2belianroupsExactness,irectums,Freebelianroups)3omotopyhapteromologyfomplexes1omplexes2onnectingomomorphism,Exactomologyequence3hain-Homotopy4reeomplexeshapteringularomology1tandardimplicesndheirinearaps2heingularomplex3ingularomology4pecialases5nvariancenderomotopy6arycentricubdivision7mallimplices.xcision8ayer-Vietorisequenceshapterpplicationsouclideanpace1tandardapsetweenellsndpheres2omologyfellsndpheres3ocalomology4heegreefap5ocalegrees6omologyropertiesfeighborhoodetractsnRn7ordanheorem,nvariancefomain8uclideaneighborhoodetractsENRs)hapterellularecompositionndellularomology1ellularpaces2W-Spaces3xamples4omologyropertiesfW-Spaces5heuler-Poincareharacteristic6escriptionfellularhainapsndfheellularoundaryomomorphism7implicialpaces8implicialomologyhapterunctorsfomplexes1odules2dditiveunctors3erivedunctors4niversaloefficientormula5ensorndorsionroducts6omndxt7ingularomologyndohomologyitheneraloefficientroups8ensorproductndilinearity9ensorproductfomplexesunnethormula10ornfomplexes.omotopylassificationfhainaps11cyclicodels12heilenberg-Zilberheorem.unnethormulasorpaceshapterroducts1hecalarroduct2hexterioromologyroduct3henterioromologyroduct(Pontrjaginroduct4ntersectionumbersnRn5heixedointndex6heefschetz-Hopfixedointheorem7hexte