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Feller Vol. 1 is considered the classic text for discrete probability: https://epubs.siam.org/doi/10.1137/1011021

Volume 2 is easily found as a pdf on google, but it's much harder.

Both Feller volumes have some good stuff. E.g., volume 2 has the renewal theorem -- roughly, arrivals from many independent sources look like a Poisson process, i.e., times between arrivals are independent identically distributed random variables with exponential distribution where the parameter in the distribution is the arrival rate. E.g., expect that between 1 PM and 2 PM, arrivals at a popular Web site will be Poisson, and might use that for capacity planning or anomaly detection.

But as my main probability prof summarized, an unguided tour of Feller is not promising. I believe he was correct. Look elsewhere for the first intuition, common applications, or the high quality math, e.g., based on sigma algebras and the Radon-Nikodym theorem, the limit theorems -- laws (weak and strong) of large numbers, central limit theorem (the strong Lindeberg-Feller version, irony here), the ergodic theorem, martingales, Skorohod representation, Kolomogorov extension theorem, Lebesgue decomposition, etc.

Feller is damn hard work. I'd put feller's probability on the same level as Rudin's real analysis.

Agree Feller is excellent. I don't think it has much in the way of prerequisites and comes at probability from a solid "fundamental understanding" POV.

Volume 2 is more difficult but also very good.

Don't forget that you always read mathematics ( or probability theory ) with a pencil in hand. It's a participatory activity.

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