2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/128532A mathematical introduction to the classical solutions of noncommutative field theory is presented, with emphasis on how they may be understood as states of D-branes in Type II superstring theory. Both scalar field theory and gauge theory on Moyal spaces are extensively studied. Instantons in Yang-Mills theory on the two-dimensional noncommutative torus and the fuzzy sphere are also constructed. In some instances the connection to D-brane physics is provided by a mapping of noncommutative solitons into K-homology.48 pages; Based on minicourse given at the International Workshop on Noncommutative Geometry NCG2005, Institute for Studies in Theoretical Physics and Mathematics (IPM), Tehran, Iran, September 11-22 2005. To be published in the minicourse volume by World Scientific and in IPM Lecture Notes Series; v2: References added; v3: Minor correctionsHigh Energy Physics - TheoryMathematical Physicstext