Advice: Modern vs. Classics First of all, my apologies if (well, I know I am but I don't know where to put it) I am posting this in the wrong place. So please feel free to move it to someplace else or to tag it differently if that is possible. 
Anyways, I've been reading Lang's Linear Algebra and Lang's Undergraduate Algebra and I feel that they might not be the books I was looking for. They don't seem to be thorough enough and even though I have really been enjoying Lang's style I've started to look for other texts to use instead. I've narrowed it down to Hoffman & Kunze vs. Friedberg, Insel & Spence for Linear Algebra and for Abstract Algebra to Artin vs. Dummit & Foote, but I'm having troubles deciding which ones to go with. I've looked at reviews for all of them and they all seem to be great books and exactly what I'm looking for, but I don't know which ones to take as the main ones for reading. Can anyone who is familiar with these help me decide? What are the differences between each book in each set? These are both for self-study and abstraction isn't a real issue. 
Thank-you. 
 A: Every good book will contain stuff another good book omits, and the choice is often made on one's personal preferences.
Artin is essentially an undergraduate text combining linear algebra and abstract algebra, with some graduate topics like representation theory and a great emphasis on matrices and geometry. If you want a not so conventional text that covers interesting topics like symmetry groups, go for Artin.
Dummit treats only abstract algebra, but covers all basic topics from undergraduate to beginning graduate level, while Hoffman and Friedberg treat only linear algebra.
A: Even though you've decided, perhaps I can add my two cents (or Bitcoins). For algebra, I think Artin is superior in learning the principles of group theory. To that end here is a link to great video lectures by Benedict Gross (Harvard) that follows Artin:
http://www.extension.harvard.edu/open-learning-initiative/abstract-algebra
For rings and fields Dummit & Foote is the best choice. (Probably because of two authors.)
For linear algebra, I prefer "Linear Algebra Done Right" (if you can get past the title). It is a rigorous approach and will greatly benefit your endeavors in algebra if you make some headway in it first. When you get to certain topics in algebra, you will be happy you have familiarity with concepts such as vector space, basis, null set (aka the kernel), etc.
When you get rolling, you will get a great deal out of these short pieces by Keith Conrad (Connecticut) on topics in these areas as you encounter them:
http://www.math.uconn.edu/~kconrad/blurbs/
