Now available in a fully revised and updated new edition, this well established textbook provides a straightforward introduction to the theory of probability. The presentation is entertaining without any sacrifice of rigour; important notions are covered with the clarity that the subject demands. Topics covered include conditional probability, independence, discrete and continuous random variables, basic combinatorics, generating functions and limit theorems, and an introduction to Markov chains. The text is accessible to undergraduate students and provides numerous worked examples and exercises to help build the important skills necessary for problem solving. INDICE 1. Probability 2. Conditional probability and independence 3. Counting 4. Random variables: distribution and expectation 5. Random vectors: independence and dependence 6. Generating functions and their applications 7. Continuous random variables 8. Jointly continuous random variables 9. Markov chains Appendix.