>>864
As you said, I am probably going to cover Amann and Escher quite a bit sooner. I think people scared me into thinking that analysis is more demanding than it probably is. 
I also thought that set theory and logic are more basic in some sense than they are. But it seems to me like you only need basic logic (basic propositions, quantificators and so on) and just the very basics of set theory (sets, operations on sets, partitions and such) to cover math to a decently advanced level. 

Thank you for the other recommendations as well.

>>866
101 problems in algebra I thought was okay. The difficulty of the problems differs quite a bit since I solved some in minutes and others left me confused even after checking the solutions. 
Some of the explanations I didn't like at all. They don't explain the thought process and sometimes just begin the solution like this:

Since (critical part of the solution that greatly simplifies the problem) holds. We know that x  is equivalent to y. Therefore z and therefore the statement is proved.