A completely revised and expanded edition, 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, a fusion of a classical branch of mathematics (summability theory) with a modern branch of analysis (ultrametric analysis). Three entirely new chapters explore sequence spaces and summability matrices. The book will appeal to both young researchers and more experienced mathematicians who are looking to explore new areas in analysis, as well as those who wish to specialize in ultrametric summability theory.