Thisbookisintendedtoserveasatextbookforacourseinalgebraictopologyatthebeginninggraduatelevel.Themaintopicscoveredaretheclassificationofcompact2-manifolds,thefundamentalgroup,coveringspaces,singularhomologytheory,andsingularcohomologytheory(includingcupproductsandthedualitytheoremsofPoincareandAlexander).ItconsistsofmaterialfromthefirstfivechaptersoftheauthorsearlierbookAlgebraicTopology:AnIntroduction(GTM56)togetherwithalmostallofhisbookSingularHomologyTheory(GTM70).Thismaterialfromthetwoearlierbookshasbeenrevised,corrected,andbroughtuptodate.Thereisenoughhereforafull-yearcourse.
Theauthorhastriedtogiveastraightforwardtreatmentofthesubjectmatter,strippedofallunnecessarydefinitions,terminology,andtechnicalmachinery.Hehasalsotried,whereverfeasible,toemphasizethegeometricmotivationbehindthevariousconcepts.Severalapplicationsofthemethodsofalgebraictopologytoconcretegeometrical-topologicalproblemsaregiven(e.g.,Brouwerfixedpointtheorem,Brouwer-Jordanseparationtheorem,lnvarianceofDomain.Borsuk-UlamtheoremS.