Some answers mention problem books (quite different from standard-format textbooks in that they consist almost entirely of problems and their solutions). Such books have been widely used in Eastern Europe at every level of education (at least when I was getting it). Let me add another one to the list:
MR0447533
Krzyż, Jan G.
Problems in complex variable theory.
Translation of the 1962 Polish original. Modern Analytic and Computational Methods in Science and Mathematics, No. 36. American Elsevier Publishing Co., Inc., New York; PWN---Polish Scientific Publishers, Warsaw, 1971. xvii+283 pp.
In his foreword, the author states: ``Most exercises are just examples illustrating basic concepts and theorems, some are standard theorems contained in most textbooks. However, the author does believe that the reconstruction of certain proofs could be instructive and is possible for an average mathematics student."
Besides standard material, there is a collection of quirky little facts in e.g. non-Euclidean geometry in the disk or logarithmic potential theory (and much more). All stated as problems for the reader to solve. However, many solutions are included.
There were subsequent editions in Polish. I used one as an undergraduate student and still have a copy.
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