B. P. Demidovich - Problems on Multivariate Analysis (approximate translation). A very tough book about analysis on $\mathbb{R}^n$; in fact all problems 'can' be solved by first or seond-year students, but it's got lots of tricky questions that will not let you sleep at night. Only the best need apply - the book gives you the most basic definitions and then throws you out with a broken pontoon in the middle of the ocean, at night. I believe the writer is Russian or Belorussian, I have only encountered a few tattered copies that have been doing the rounds between students for a decade at least. Haven't found a better book for tough multivariate analysis.