TITLE: Are there any books that take a 'theorems as problems' approach?
QUESTION [57 upvotes]: Are there any books that present theorems as problems? To be more specific, a book on elementary group theory might have written: "Theorem: Each group has exactly one identity" and then show a proof or leave it as an exercise. The type of book that I am imagining would have written "Problem: How many unit elements can a group have?" and similarly for all other theorems.

REPLY [3 votes]: "Selected Problems in Real Analysis" by M. G. Goluzina, A. A. Lodkin, B. M. Makarov, A. N. Podkorytov. (The authors are modest with the title, I would rather say that this book contains all problems in real analysis.) This is a perfect complement to Polya and Szego, whose book is rather on complex analysis.