F. Prus-Wisniowski - Szeregi Rzeczywiste (Poland, Uniwersytet Szczecinski) - a monograph on real series. It can be read by first-year students while supplying the reader with very powerful tools for real (and sometimes complex) series; it might surprise the PhD reader. More importantly, it builds a good understanding of the way real series work.Publisher's website
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.
I.N. Bronstein, K.A. Semyendayev - Mathematics Handbook - an awesome, very complete mathematics handbook for applied mathematicians, physicists, and engineers. Also useful for the pure mathematics researcher who just wants to quickly look up how a basic item in mathematics worked. This work has not lost any of its gleam since it was first written; numerous updates have been made; it is the reference compendium in Central and Eastern Europe. It has received prizes for being the best illustrated engineering book; indeed, the drawings are exact and even beautiful, and have not become outdated in the time of computer generated imagery. Definitely one of the books that put the Russians in outer space.Numerous German editions of the book on Amazon
G.M. Fichtenholz - Analysis (3 Tomes) - The course of real analysis for budding mathematicians beyond the Iron Curtain. Everyone knows it. It's the first book you read, and the last one you refer to before finishing your master's degree. It takes you from the definition of a set to advanced multivariate calculus; it gives you a lot of tools for classical mechanics in the meantime. It is so trustworthy that the single wrong theorem that it contained caused a telltale student to fail his dissertation, because neither he nor his professor checked the proof and they based the whole thesis on the false premise - that was a decade or two ago and the book is, right now, free of errors. Originally in Russian. Another book that kept the Russians strong during the cold war.Wikipedia entry about the author G. Banaszak, W. Gajda - Elementy Algebry Liniowej (Elements of Linear Algebra), Poland, WNT - 2 tomes - Don't let the name fool you. This recent publication has more linear algebra than you can shake a stick at. It's a very comprehensive course of linear, and some abstract, algebra; very beautifully printed, lots of decorative markup. The book is very well structured, but is not easy and requires the reader to be fully aware of what's going on. It can be a bit of a mind wringer, but on the other hand that can force you to look at many things from the writers' - quite original sometimes - viewpoint.
