Introduction to Topology
Topological spaces and continuous functions form the backbone of this MIT course, which builds up the concepts underlying modern analysis and geometry. Lectures and problem sets move through connectedness, compactness, and the separation axioms before turning to more advanced material, including function spaces, metrization theorems, embedding theorems, and the fundamental group. Materials follow the MIT OpenCourseWare format: lecture notes, assignments, and exams, available to study at your own pace with no enrollment or fee required. The course suits students who have completed a real analysis sequence and want the rigorous point-set foundations that later support algebraic topology and differential geometry. No certificate is offered, but all course content is free to use under MIT's open license.