Ben Lambert's "A student's guide to Bayesian Statistics" as the best intro to *applied* Bayesian stats. The book starts with very little prerequisites, explains the math well while keeping it to a minimum necessary for intuition, (+has good illustrations) and goes all the way to building models in Stan. (Other good books are McEarlath Statistical Rethinking, Kruschke's Doing Bayesian Data Analysis and Gelman's more math-heavy Bayesian Data Analysis). I recommend Lambert for being the most holistic coverage.
PS. He has a playlist of complementary videos to go along with the book
ETA: I have read McEarlath Statistical Rethinking and Kruschke's Doing Bayesian Data Analysis, skimmed Gelman's Bayesian Data Analysis. Recommend Lambert if you only read 1 book or as your first book in the area.
I think it's actually still better to post the comments in the original thread, just to have everything be in one place, and now that it's pinned for a week, the new comments will get seen (and generally get more visibility than here).
Having the rules in the post made me think you wanted new suggestions in this thread. The rest of the post and habryka's comment point towards new comments in the old thread.
If you want people to update the old thread, I would either remove the rules from this post, or add a caveat like "Remember, when you go to post in that thread, you should follow the rules below"
A reddit thread on the best introductions to a field or industry, which might make a good addition to this list:
https://www.reddit.com/r/AskReddit/comments/c4glci/professionals_and_experts_of_reddit_what_is_the
I notice the links to one of the recommended econ textbooks now seems to go to a somewhat dubious short term loan site. I recalled previously one had linked to a fully free textbook.
I occasionally refer back to lukeprog's Best Textbooks on Every Subject post. I thought it might be a good idea to direct people back to it in the hopes of updating the list, for the following reasons:
At ChristianKI's suggestion: