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.
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.