Of you prefer an even more entertaining approach and a very gentle introduction into the topic, I recommend the comic "Logicomix" which tells Russel's journey (though not historically correct all the time for story telling reasons).
Logicomix is novel, and done well, but flawed … it's deficiencies lie in what it leaves out which may come across as an unfair charge but in this case the charge is warranted. There is a more historically correct and less orthodox work waiting in the wings for whosoever should attempt it.
Just got this from the library, it's a real page turner. Heard about it in this excellent interview: https://www.typetheoryforall.com/episodes/goedel-s-incomplet...