: More Group Theory (7), Bilinear Forms (8), Linear Groups (9), Group Representations (10), Rings (11), Factoring (12), Quadratic Number Fields (13), Linear Algebra in a Ring (14), and Fields (15). Digital Availability

Don’t skip Chapters 1–2 (Matrices) and 4 (Vector Spaces). Artin builds group theory out of matrix theory. Read with a notebook. Redraw every matrix multiplication by hand.

Michael Artin's is widely considered a masterpiece of modern mathematical exposition, particularly for its ability to weave linear algebra into the broader study of abstract structures like groups, rings, and fields. Why Artin’s "Algebra" is Highly Regarded