Modern Geometry - Methods and Applications: Part 3: Introduction to Homology Theory

I first got acquainted with Dubrovin/Novikov/Fomenko collection when I was still a second year (sophomore in the US system) student in Math-Phystrying to learn the basics on plane/space differential curves as acomplement for my Calculus courses. And since then I've made countless references to this book and its siblings.The pace is fast compared toother well known introductions on differential geometry/topologybut the text has many insightful and non-trivial examplesexamples. Challenging problems are present everywhere in the text!Though there are a few problems per chapter, the problems sometimes reallyrequire some mastery of the material being far from immediateapplications of the theory developed(for the joy or despair of thereader). Intentionally the authors try, whenever possible, to replace calculations anddifficult deductions with conceptual proofs. Frequent links withphysical theories (e.g. mechanics, electromagnetism, generalrelativity, field theory etc.) compound a good deal of the textwhich makes its reading still more delightful. As a con, I wouldsay the text is quite hard for a beginner but stubborness pays-off in this case.The second volume of this series covers differential topology w/ emphasis on many aspects of modern physics, like GR, solitons and Yang-Mills theory. There's also a nice account on complex manifolds, mainly Riemman surfaces and it's relation to Abel's thm. Among other topics: classification of compact surfaces , hyperbolic geometry etc.The third volume covers Homology theory and included a readable account of Spectral sequences for those who may need to learn the machinery for qualifications exams and or applications of complex geometry to contemporary physics (e.g. twistor theory). Viktor Prasolov has recently published a treatise on Homology with more problems and more rigorous proofs. A nice complement to Novikov's exposition.Eclectic, but at the same time superb.