This is the second edition of "p-adic Numbers, p-adic Analysis, and Zeta-Functions" by Neal Koblitz. The book is part of the Graduate Texts in Mathematics series. The main revisions in this edition include expanding the treatment of p-adic functions in Chapter IV to include the Iwasawa logarithm and the p-adic gamma-function, rearranging and adding exercises, including an extensive appendix with answers and hints to the exercises, and numerous corrections and clarifications. The book is intended as an introduction to p-adic analysis at an elementary level, requiring minimal background knowledge. It aims to develop basic ideas of p-adic analysis and present two significant applications: Mazur's construction of the Kubota–Leopoldt p-adic zeta-function and Dwork's proof of the rationality of the zeta-function of a system of equations over a finite field. The book highlights analogies and contrasts with classical calculus concepts. It omits more advanced topics such as the Hasse–Minkowski Theorem and Tate's thesis, focusing instead on a selection of material suitable for undergraduates or beginning graduate students in a one-term course. The exercises are designed to help students grasp the material and are not overly difficult. The book is of interest to students in number theory, representation theory, and algebra, as p-adic analysis bridges classical analysis with algebra and number theory. The logical dependence of chapters is 2, 1, 3, 4, 5. The book includes a bibliography, answers and hints for the exercises, and an index.This is the second edition of "p-adic Numbers, p-adic Analysis, and Zeta-Functions" by Neal Koblitz. The book is part of the Graduate Texts in Mathematics series. The main revisions in this edition include expanding the treatment of p-adic functions in Chapter IV to include the Iwasawa logarithm and the p-adic gamma-function, rearranging and adding exercises, including an extensive appendix with answers and hints to the exercises, and numerous corrections and clarifications. The book is intended as an introduction to p-adic analysis at an elementary level, requiring minimal background knowledge. It aims to develop basic ideas of p-adic analysis and present two significant applications: Mazur's construction of the Kubota–Leopoldt p-adic zeta-function and Dwork's proof of the rationality of the zeta-function of a system of equations over a finite field. The book highlights analogies and contrasts with classical calculus concepts. It omits more advanced topics such as the Hasse–Minkowski Theorem and Tate's thesis, focusing instead on a selection of material suitable for undergraduates or beginning graduate students in a one-term course. The exercises are designed to help students grasp the material and are not overly difficult. The book is of interest to students in number theory, representation theory, and algebra, as p-adic analysis bridges classical analysis with algebra and number theory. The logical dependence of chapters is 2, 1, 3, 4, 5. The book includes a bibliography, answers and hints for the exercises, and an index.