by Rick Durrett
I have learnt probability from this book and even now, doing research in Probability, I see myself getting back to this book from time to time. It is straight to the point and it is the kind of book that “contains what is really important”. Thus, this is a good book for reference, but I understand that it can be a tough book for a first course in probability.
You can download the book on Professor Durrett’s webpage.