Besides various corrections, additions, and deletions of material in the first edition, added emphasis has been placed on the geometrical frame- work of permutation methods. When ordinary Euclidean distance replaces commonly-used squared Euclidean distance as the underlying distance func- tion, then concerns such as robustness all but vanish. This geometrical em- phasis is primarily discussed and motivated in Chapters 1 and 2. Chapter 3 now addresses multiple binary choices and also includes a real data example that demonstrates an exceedingly strong association between heavy metal soil concentrations and academic achievement. Multiple binary choices are also placed in the randomized block framework of Chapter 4. Whereas the main addition to Chapter 5 is the generalization of MRPP regression analyses from univariate multiple linear regression in the first edition to multivariate multiple linear regression in the second edition, further clar- ification is made between the exchangeable random variable approach of MRPP regression analyses and the independent random variable approach of other analyses, such as the Cade–Richards regression analyses. Chapter 6 now includes an efficient approach due to L. Euler for obtaining exact goodness-of-fit P-values when equal probabilities occur. A resampling ap- proach is now included for r-way contingency tables in Chapter 7, along with an investigation of log-linear analyses involving small sample sizes. While only a few minor changes occur in Chapter 8, a new Chapter 9 in- cludes (1) a discrete analog of Fisher’s continuous method for combining P -values, (2) a Monte Carlo investigation of Fisher’s Z transformation, and (3) a new multivariate test for similarity between two samples.