An extensive list is at <A HREF="https://math.stackexchange.com/questions/306828/list-of-problem-books-in-undergraduate-and-graduate-mathematics">MSE</A>, including pointers to dedicated web sites, such as <A HREF="http://www.mathpropress.com/mathBooks/">this one.</A> A particularly comprehensive collection is in <A HREF="https://books.google.nl/books?id=bm9lBglsZhsC&printsec=frontcover&hl=nl&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false">Problems and Solutions in Mathematics</A>, with a list of advanced topics (including Galois theory, homotopy/homology, differential geometry of manifolds, measurability and measure, PDE's).

I might add 

<A HREF="https://archive.org/details/TheStanfordMathematicsProblemBook">The Stanford Mathematics Problem Book</A> by George Polya and Jeremy Kilpatrick.

> These 20 sets of intriguing problems test originality and insight
> rather than routine competence. They involve theorizing and verifying
> mathematical facts; examining the results of general statements;
> discovering that highly plausible conjectures can be incorrect;
> solving sequences of subproblems to reveal theory construction; and
> recognizing "red herrings," in which obvious relationships among the
> data prove irrelevant to solutions.