An Introduction to Ultrametric Summability Theory This is the second completely revised and expanded edition of the author’s first book covering numerous new topics and recent developments in ultrametric summability theory. Ultrametric analysis has emerged as an important branch of mathematics in recent years. This book presents a brief survey of the research to date in ultrametric summability theory which is a fusion of a classical branch of mathematics (summability theory) with a modern branch of analysis (ultrametric analysis). Several mathematicians have contributed to summability theory as well as functional analysis. The book will appeal to both young researchers and more experienced mathematicians who are looking to explore new areas in analysis. The book is also useful as a text for those who wish to specialize in ultrametric summability theory 1. Introduction and Preliminaries 2. Some Arithmetic and Analysis in Qp; Derivatives in Ultrametric Analysis 3. Ultrametric Functional Analysis 4. Ultrametric Summability Theory 5. The Nörlund and the Weighted Mean Methods 6. The Euler and the Taylor Methods 7. Tauberian Theorems 8. Silverman Toeplitz Theorem for Double Sequences and Double Series 9. The Nörlund Method and the Weighted Mean Method for Double Sequences