**Newer Books**

*Matrix Analysis and Applied Linear Algebra* by Meyer is very well written with clear cut examples and exercises.  I think this would make an excellent first course.

I agree also that Axler's books is a great text for the more mature.

**Classics**

*Finite-Dimensional Vector Spaces* by P. R. Halmos is an absolute essential for the budding mathematician in my opinion.  This is because of the exercises (My recommendation: solve all of them).

As mentioned above
*Linear Algebra (2nd Edition)* by Kenneth M Hoffman and Ray Kunze.  This may be my favorite text because of its volume of content.

**More Advanced**

*Advanced Linear Algebra* by Steven Roman 

**Matrix Analysis**

*Matrix Analysis* and *Topics in Matrix Analysis* by Roger A. Horn and Charles R. Johnson 

*Matrix Analysis* by Rajendra Bhatia