Linear algebra
Linear algebra is perhaps the most important tool for modern science: quantum mechanics, data analysis, machine learning, …All use linear algebra in one way or another.
This was my curriculum in the first linear algebra course I took. I think it is a very good book, and highly readable. What it lacks, is the consideration of general finite dimensional linear vector spaces.
An online textbook in linear algebra by Robert A. Beezer can be found here: http://linear.ups.edu/. It is free, and also has great sets of exercises. PDF versions here: http://linear.ups.edu/download.html
This book by the great Paul Halmos is old, by very comprehensive. I find it quite readable, and have used it many times. I would consider the level to be more advanced than Fraleigh and Beauregard.