The most function of this publication is to provide a scientific therapy of singular homology and cohomology conception. it truly is in a few feel a sequel to the author's prior publication during this Springer-Verlag sequence entitled Algebraic Topology: An creation. This past booklet is well now not a logical prerequisite for the current quantity. even though, it can definitely be effective for a potential reader to have an acquaintance with a few of the subject matters handled in that past quantity, equivalent to 2-dimensional manifolds and the funda psychological staff. Singular homology and cohomology thought has been the topic of a couple of textbooks within the final couple of a long time, so the fundamental define of the speculation in all fairness good proven. for that reason, from the viewpoint of the maths concerned, there might be little that's new or unique in a e-book comparable to this. nonetheless, there's nonetheless room for loads of sort and originality within the info of the exposition. during this quantity the writer has attempted to offer a simple therapy of the subject material, stripped of all pointless definitions, terminology, and technical equipment. He has additionally attempted, at any place possible, to stress the geometric motivation at the back of a number of the strategies.