Algebraic Topology I
MIT OpenCourseWare offers this graduate level course on singular homology of topological spaces. The syllabus covers singular homology, CW complexes, homological algebra, cohomology, and Poincare duality, building from the basic machinery of algebraic topology toward the tools used to distinguish spaces up to homotopy equivalence. Materials include lecture notes, problem sets, and exam materials used in MIT's own classroom, free to access and download under a Creative Commons license. The course assumes prior exposure to point-set topology and abstract algebra and is meant as a first serious treatment of homology theory rather than an introduction to topology itself. There is no instructor interaction or certificate, only the self-study materials MIT has released, which are detailed enough to follow the same sequence a graduate student at MIT would encounter in the classroom.