These are the foundation of linear algebra, focusing on scaling and adding "arrows" or coordinates, built on top of the rules of fields. Why It Matters
by Charles Pinter (Available very cheaply or through many university libraries). To help you get the exact material you need: The specific edition or author (if not Gilbert & Gilbert) Elements of Modern Algebra free ebook download
(I can help you check for an institutional login) These are the foundation of linear algebra, focusing
by Thomas Judson (The gold standard for free algebra texts). Elements of Modern Algebra free ebook download
you're struggling with (e.g., Sylow Theorems, Galois Theory)
Modern algebra (or abstract algebra) moves away from solving for