The Cauchy-Schwarz Master Class

Seconding Steele (cf. my comment)

The Cauchy-Schwarz Master Class by J. Michael Steele Linear Algebra by A.O. Morris (out of print and tricky to find)

Steele's The Cauchy-Schwarz Masterclass is actually quite good and seemingly designed for self study. (A lingering result of this book is I heavily use inequalities even outside of analysis.) Artin's Algebra probably has had the most impact on my math thinking. The development of groups and rings while tightly linking them to linear algebra was rather brilliant.

Best books I read in 2011: * "Salonica, City of Ghosts" by M.Mazower. Tells the history of Thessaloniki, informative, entertaining, at times nostalgic. * "The Cauchy-Schwarz Master Class" by J.M.Steele. A guided tour of mathematical inequalities. Very entertaining and readable (for a math book) and extremely well written. * "Indiscrete Thoughts" by G-C.Rota. Irreverent anecdotes about mathematicians. * "Black Swan" by N.N.Taleb. Maybe overhyped and at times annoying and pompous, but extremely insightful nevertheless.