TITLE: Best book for self-study on the foundations of probability
QUESTION [7 upvotes]: After some selection, I have three "candidates" books to purchase in order to study by myself the foundations of the theory of probability, at a level that I can define as "high undergraduate"/"low graduate". These are my candidates:
1) Probability. A.N.Shiryaev. GTM Springer-Verlag.
2) Probability and Stochastics. Erhan Çinlar. GTM Springer-Verlag.
3) Probability Theory. A. Borovkov. UT Springer-Verlag. 
I have very good references from all of them.
Which one do you recommend me ?
Thank you for your answers.

REPLY [7 votes]: I would reccomend just using lecture notes available online. That way you have no risk from purchasing a book.
Some good ones:
http://www.math.nyu.edu/faculty/varadhan/limittheorems.html 
http://www-stat.stanford.edu/~adembo/stat-310a/lnotes.pdf
https://ocw.mit.edu/courses/mathematics/18-175-theory-of-probability-spring-2014/lecture-slides