Homological Methods in Noncommutative Geometry
by D. Kaledin
Number of pages: 77
The first seven lectures deal with the homological part of the story (cyclic homology, its various definitions, various additional structures it possesses). Then there are four lectures centered around Hochschild cohomology and the formality theorem.
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by Masoud Khalkhali - University of Western Ontario
Contents: Introduction; Some examples of geometry-algebra correspondence; Noncommutative quotients; Cyclic cohomology; Chern-Connes character; Banach and C*-algebras; Idempotents and finite projective modules; Equivalence of categories.
by Igor Nikolaev - arXiv
The book covers basics of noncommutative geometry and its applications in topology, algebraic geometry and number theory. Intended for the graduate students and faculty with interests in noncommutative geometry; they can be read by non-experts.
by Alain Connes - Academic Press
The definitive treatment of the revolutionary approach to measure theory, geometry, and mathematical physics. Ideal for anyone who wants to know what noncommutative geometry is, what it can do, or how it can be used in various areas of mathematics.
by Nigel Higson, John Roe - American Mathematical Society
These lectures are intended to introduce key topics in noncommutative geometry to mathematicians unfamiliar with the subject. Topics: applications of noncommutative geometry to problems in ordinary geometry and topology, residue index theorem, etc.