The most important revision in the second edition are the enlargment of the treatment of p-adic functions in Ch. 4 to include the Iwasawa logarithm and the p-adic gamma-function, the rearrangement and addition of some exercises, the inclusion of an extensive appendix of answers and hints to the exercises, and numerous corrections and clarifications. The first edition has become the standard introduction to the theory of p-adic numbers on the advanced undergraduate and beginning graduate level.