How to learn about interesting topics in a small group of people?
It seems very useful to broaden your mathematical background and get to know topics that are away from your field of specialization.
For instance, in philosophy, you can just gather some interested fellow students, pick a book, meet regularly and read some pages and discuss the content. Afterwards, you (hopefully) will have a reasonable knowledge of the arguments and theories sketched in the book. This is often done by people I know, and I have participated myself and enjoyed it a lot.
With mathematics this is more a problem, for many reasons. You often need more time for the same amount of text, it is hard to discuss proofs you don't really know yet, interesting examples require a lot of careful thinking, ...
Maybe there are some books or other resources that are well suited? Maybe some topics that are (in this way) better accessible than others? How should such a group be (or not be) organized?
Two comments: Of course, one could prepare little presentations, read a lot in advance and so on. But then it is almost self-study, so that's not what I mean. Also, we may assume the members of this reading circle have good knowledge of undergraduate mathematics.
Thank you in advance.