Yes, and yes.
A classic text is Li and Vitanyi “An Introduction to Kolmogorov Complexity and it’s Applications”—see: http://homepages.cwi.nl/~paulv/kolmogorov.html
If you want an online (condensed) version but without the formal proofs, then have a look at: http://www.scholarpedia.org/article/Algorithmic_probability
Yes, and yes.
A classic text is Li and Vitanyi “An Introduction to Kolmogorov Complexity and it’s Applications”—see: http://homepages.cwi.nl/~paulv/kolmogorov.html
If you want an online (condensed) version but without the formal proofs, then have a look at: http://www.scholarpedia.org/article/Algorithmic_probability