Probability theory is essential for statistics, machine learning, finance, and physics. These books cover everything from combinatorial probability through measure theory and stochastic processes.
Introductory Probability
Standard introductory probability textbooks.
| Book | Author | Year | Level | Description |
|---|---|---|---|---|
| Introduction to Probability 2nd Edition, CRC Press | Joseph K. Blitzstein, Jessica Hwang | 2019 | Intermediate | Harvard's Stat 110 textbook, the best modern introduction to probability. Free lectures on YouTube. |
| A First Course in Probability 10th Edition, Pearson | Sheldon M. Ross | 2018 | Beginner-Intermediate | The most widely used introductory probability textbook. |
| Introduction to Probability 2nd Edition, Athena Scientific | Dimitri P. Bertsekas, John N. Tsitsiklis | 2008 | Intermediate | MIT-based textbook with strong emphasis on conditioning and intuition. |
Measure-Theoretic Probability
Rigorous graduate-level probability based on measure theory.
| Book | Author | Year | Level | Description |
|---|---|---|---|---|
| Probability: Theory and Examples 5th Edition, Cambridge | Rick Durrett | 2019 | Advanced | The standard graduate probability textbook, freely available. Rigorous measure-theoretic treatment with many examples. |
| Probability and Measure Anniversary Edition, Wiley | Patrick Billingsley | 2012 | Advanced | Classic rigorous probability textbook. |
| Foundations of Modern Probability 2nd Edition, Springer | Olav Kallenberg | 2002 | Advanced | Comprehensive advanced probability reference. |
Stochastic Processes
Markov chains, martingales, and Brownian motion.
| Book | Author | Year | Level | Description |
|---|---|---|---|---|
| Introduction to Stochastic Processes 2nd Edition, Chapman & Hall | Gregory F. Lawler | 2006 | Advanced | Clear introduction to major stochastic processes. |
| Markov Chains and Mixing Times 2nd Edition, AMS | David A. Levin, Yuval Peres | 2017 | Advanced | Modern treatment of Markov chains with mixing time focus. Free online. |
| Brownian Motion and Stochastic Calculus 2nd Edition, Springer | Ioannis Karatzas, Steven E. Shreve | 1998 | Advanced | Standard reference on Brownian motion and stochastic integration. |
Applied Probability
Probability with applications to specific domains.
| Book | Author | Year | Level | Description |
|---|---|---|---|---|
| Probability and Random Processes 3rd Edition, Oxford | Geoffrey Grimmett, David Stirzaker | 2001 | Intermediate-Advanced | Broad coverage of probability and stochastic processes. |
| Introduction to Probability Models 12th Edition, Academic Press | Sheldon M. Ross | 2019 | Intermediate | Applied probability emphasizing stochastic models. |
| Stochastic Processes 3rd Edition, Wiley | Sheldon M. Ross | 1995 | Intermediate-Advanced | Classic applied stochastic processes textbook. |
Probability for ML and Physics
Probability with specific applications to machine learning and physics.
| Book | Author | Year | Level | Description |
|---|---|---|---|---|
| Information Theory, Inference, and Learning Algorithms Cambridge | David J.C. MacKay | 2003 | Advanced | Unique integrated treatment of information theory and ML. Free PDF. |
| Probabilistic Graphical Models MIT Press | Daphne Koller, Nir Friedman | 2009 | Advanced | Definitive treatment of probabilistic graphical models. |
| High-Dimensional Probability Cambridge | Roman Vershynin | 2018 | Advanced | Modern probability for data science and ML applications. |