A study group for people who want to understand the continuum hypothesis, forcing, etc.... we are going to be using Nik Weaver's Forcing for Mathematicians (https://www.amazon.com/dp/B00XKN8JHU/ref=dp-kindle-redirect?_encoding=UTF8&btkr=1). It is a recommended introduction to forcing including applying it to the continuum hypothesis. We meet every two weeks or after having studied a small section of the book to get together and discuss it, make sure we all understand it, talk about some of the philosophy behind it, excetera.
Please note - when this group was launded, we were using Paul Cohen's book ( https://www.amazon.com/Theory-Continuum-Hypothesis-Dover-Mathematics/dp/0486469212 ). However, we found out that the version of forcing Cohen discusses, since he had just invented it, is no the modern version. Hence, we decided to start using a more modern book.