This paper explores the connection between noncommutative geometry and string theory, particularly in the presence of a nonzero B-field. The authors show that string dynamics can be described by a minimally coupled (supersymmetric) gauge theory on a noncommutative space in certain limits. They discuss the equivalence between ordinary and noncommutative gauge fields, which is realized through a change of variables. This change is verified by comparing the Dirac-Born-Infeld theory with its noncommutative counterpart. The paper also examines noncommutative gauge theory on a torus, T-duality, and Morita equivalence. It discusses the D0/D4 system, the relation to M-theory in DLCQ, and a possible noncommutative version of the six-dimensional (2,0) theory. The paper begins by reviewing the idea that spacetime coordinates do not commute, a concept with a long history in both mathematics and physics. It discusses the use of noncommutative geometry in string theory, particularly in the context of toroidal compactification and the matrix model of M-theory. The authors then explore the role of T-duality in noncommutative Yang-Mills theory, which acts within the framework rather than mixing with stringy excitations. They also discuss the role of Morita equivalence in establishing T-duality and the relation to the Dirac-Born-Infeld Lagrangian. The paper then focuses on the behavior of open strings in the presence of a constant B-field. It shows that the B dependence of the effective action can be described by making spacetime noncommutative. The authors demonstrate that for large B or small α', the physics can be described by noncommutative Yang-Mills theory. They also show that the effective action can be derived from the S-matrix, and that the B-dependence is described by replacing ordinary products with * products. The paper concludes by discussing the implications of these results for the effective action in the α' → 0 limit. It shows that the effective action reduces to the * product of fields, and that the B-dependence is described by replacing F with F + B. The authors also discuss the relationship between different regularizations of the same quantum field theory and the necessity of field redefinitions to compare different descriptions. The paper highlights the importance of the zero slope limit in simplifying the effective action and the role of noncommutative geometry in describing string theory in the presence of a B-field.This paper explores the connection between noncommutative geometry and string theory, particularly in the presence of a nonzero B-field. The authors show that string dynamics can be described by a minimally coupled (supersymmetric) gauge theory on a noncommutative space in certain limits. They discuss the equivalence between ordinary and noncommutative gauge fields, which is realized through a change of variables. This change is verified by comparing the Dirac-Born-Infeld theory with its noncommutative counterpart. The paper also examines noncommutative gauge theory on a torus, T-duality, and Morita equivalence. It discusses the D0/D4 system, the relation to M-theory in DLCQ, and a possible noncommutative version of the six-dimensional (2,0) theory. The paper begins by reviewing the idea that spacetime coordinates do not commute, a concept with a long history in both mathematics and physics. It discusses the use of noncommutative geometry in string theory, particularly in the context of toroidal compactification and the matrix model of M-theory. The authors then explore the role of T-duality in noncommutative Yang-Mills theory, which acts within the framework rather than mixing with stringy excitations. They also discuss the role of Morita equivalence in establishing T-duality and the relation to the Dirac-Born-Infeld Lagrangian. The paper then focuses on the behavior of open strings in the presence of a constant B-field. It shows that the B dependence of the effective action can be described by making spacetime noncommutative. The authors demonstrate that for large B or small α', the physics can be described by noncommutative Yang-Mills theory. They also show that the effective action can be derived from the S-matrix, and that the B-dependence is described by replacing ordinary products with * products. The paper concludes by discussing the implications of these results for the effective action in the α' → 0 limit. It shows that the effective action reduces to the * product of fields, and that the B-dependence is described by replacing F with F + B. The authors also discuss the relationship between different regularizations of the same quantum field theory and the necessity of field redefinitions to compare different descriptions. The paper highlights the importance of the zero slope limit in simplifying the effective action and the role of noncommutative geometry in describing string theory in the presence of a B-field.