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For the hard way, look at Bruno de Finetti's Theory of Probability:

https://onlinelibrary.wiley.com/doi/book/10.1002/97811192863...

Jaynes is certainly very deep and some sections are harder than others. It's interesting regardless of your level (this is a book worth rereading several times).

For a less technical, but full of insight, introduction see Dennis Lindley's Understanding Uncertainty:

https://onlinelibrary.wiley.com/doi/book/10.1002/97811186501...

Bayesian Data Analysis by Andrew Gelman

http://www.stat.columbia.edu/~gelman/book/

one vote for BDA. For programmers who learn better by implementing things, this book [1] is also good:

[1]: https://www.amazon.com/Bayesian-Methods-Hackers-Probabilisti...

Parts of that book are available online[1] for free. If not for that book I would never have understood how to apply Bayesian stats to problems that interested me.

[1] http://camdavidsonpilon.github.io/Probabilistic-Programming-...

Probability Theory: The Logic of Science by Edwin Jaynes

http://www.med.mcgill.ca/epidemiology/hanley/bios601/Gaussia...

But really, the first two chapters aren't that hard.

Statistical Rethinking: A Bayesian Course with Examples in R and Stan is also considered pretty good.

Thank you all!