William Feller (1906–1970)

If you were to lock me up for a year and allow only one book for the whole time, this is the book I would take with me.
The way each problem is treated is delightful. The book is slightly dated and so it is not a textbook of modern probability theory. But if you want to be hooked to probabiliistic thinking and applications of probability, this is the book.
For me, Feller's book has served as an introduction to the subject, a great reference and sometimes I look into it simply because I want show more more intuition about something.
If you are going to do research in probability, Volume 1 of Feller's book leads very naturally into Feller - volume 2, or some of the modern probability textbooks like Durrett or the two volume series on stochastic processes by Karlin and Taylor.
This is classical math at its very best. show less

This two-volume set is a wonderful introduction to the topic, with loads of fascinating examples. I still use it, forty years after my first reading of it. Cannot over-recommend!

i admit, this is as good as everything says it is.