The book "Stochastic Modelling and Applied Probability" (formerly titled "Applications of Mathematics") is a comprehensive treatise on large deviations theory, edited by B. Rozovskiǐ and G. Grimmett. The second edition, corrected from the 1998 printing, includes significant updates and new content. Key changes include: 1. **New Sections**: Added sections on concentration inequalities, a metric framework for large deviations, a weak convergence approach to large deviations, refinements of the Gibbs conditioning principle, and a complete rewrite of the section on sampling without replacement. 2. **Exercise Enhancements**: New exercises have been added to reflect interesting results not covered in the main text, and some exercises have been removed for clarity or difficulty. 3. **Theoretical Updates**: The general principles of Chapter 4 have been updated with new theorems and lemmas. 4. **Bibliography**: The bibliography has been expanded with over 100 entries to correct omissions and reflect recent advances. 5. **Historical Notes**: Historical notes have been rewritten to provide a more comprehensive overview of the field. The book is designed to be accessible to a wide range of audiences, from senior undergraduates to advanced graduate students, and covers both finite-dimensional and abstract empirical measure applications. It includes detailed exercises, historical notes, and references, making it a valuable resource for researchers and students in statistics, engineering, statistical mechanics, and applied probability.The book "Stochastic Modelling and Applied Probability" (formerly titled "Applications of Mathematics") is a comprehensive treatise on large deviations theory, edited by B. Rozovskiǐ and G. Grimmett. The second edition, corrected from the 1998 printing, includes significant updates and new content. Key changes include: 1. **New Sections**: Added sections on concentration inequalities, a metric framework for large deviations, a weak convergence approach to large deviations, refinements of the Gibbs conditioning principle, and a complete rewrite of the section on sampling without replacement. 2. **Exercise Enhancements**: New exercises have been added to reflect interesting results not covered in the main text, and some exercises have been removed for clarity or difficulty. 3. **Theoretical Updates**: The general principles of Chapter 4 have been updated with new theorems and lemmas. 4. **Bibliography**: The bibliography has been expanded with over 100 entries to correct omissions and reflect recent advances. 5. **Historical Notes**: Historical notes have been rewritten to provide a more comprehensive overview of the field. The book is designed to be accessible to a wide range of audiences, from senior undergraduates to advanced graduate students, and covers both finite-dimensional and abstract empirical measure applications. It includes detailed exercises, historical notes, and references, making it a valuable resource for researchers and students in statistics, engineering, statistical mechanics, and applied probability.