Filling the gap in knowledge of algebra Recently, I realize that my inability to solve problems, sometimes, is because I have gaps in my knowldge of algebra. For example, I recently posted a question that asked why $\sqrt{(9x^2)}$ was not $3x$ which to me was fairly embarrassing because the answer was fairly logical and something that I had missed. Furthermore, I realize that when I am solving questions, I tend to get stuck on some intermediate step because that is where most of the algebra is needed. Therefore, my question is: How can I improve algebra? What steps are needed? What books should I be practicing from? What are a few things everyone should know?

For the first year course (in maths) at my University they recommend "Basic Linear Algebra" by Blyth and Robertson and "Algebra" by Michael Artin. The first book is probably more what you're looking for.
EDIT: Just to expand, the "Basic Linear Algebra" book would cover things like why $\sqrt{9x^2} = 3x$ isn't always simply the case from very early on in the book. It is mostly "basic" linear algebra like the name suggests but it's a good read to more rigorously understand algebra.
