Geometric Algebra is fascinating, and I believe solves a large number of problems that arise from a more traditional approach to vectors, but I’ve been very disappointed with the quality of books and explanations I’ve found, most of them zooming off into abstract realms too quickly, or spending an inordinate amount of time building up a generalized theory before finally getting to something useful.
Below is an explanation of Geometric Algebra that will start with a simple two dimensional vector space, i.e. ℝ2. This will be a concise introduction to ?2, the Geometric Algebra over ℝ2, and then quickly pivot to applications in ?2. This introduction will not cover the fascinating history of GA, Clifford Algebras, or Hermann Grassman.