>>13107648I'm taking Abstract Algebra this semester and so far Rotman's book has been good, it's both rigorous and easy to read. For practice problems I've been using Herstein's "Topics in Algebra".
As for introductory Linear Algebra, I'd go with Friedberg. It has a good balance of theory and applications and it's very readable. I think Shilov is a bit too dense. Hoffman it's a classic but probably a little difficult for a first course in Linear Algebra. Either way, it's always good to learn from different sources :)
