2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/126537We survey some aspects of the theory of noncommutative manifolds focusing on the noncommutative analogs of two-dimensional tori and low-dimensional spheres. We are particularly interested in those aspects of the theory that link the differential geometry and the algebraic geometry of these spaces.Survey article. Final version. To appear in the proceedings volume of the "International Workshop on Noncommutative Geometry", IPM, Tehran 2005Quantum AlgebraPrimary 58B34, 46L87; Secondary 46L89, 16S38text