Algebra I
MIT OpenCourseWare's undergraduate Algebra I covers groups, vector spaces, linear transformations, symmetry groups, bilinear forms, and linear groups. The course builds abstract algebra from group axioms through representation theory, treating symmetry groups like the dihedral and permutation groups as concrete examples before moving into vector space structure and linear maps. Materials include lecture notes, problem sets, and exams drawn from MIT's mathematics curriculum, freely downloadable under a Creative Commons license. There is no instructor interaction or graded certificate, but the full set of assignments and solutions lets a self-directed student work through the material at an undergraduate level. It suits someone who has already seen basic linear algebra and wants the more structural, proof-based treatment of groups and bilinear forms that follows it.