Mahler Functions and Transcendence This book is the first comprehensive treatise of the transcendence theory of Mahler functions and their values. Recently the theory has seen profound development and has found a diversity of applications. The book assumes a background in elementary field theory p adic field algebraic function field of one variable and rudiments of ring theory. The book is intended for both graduate students and researchers who are interested in transcendence theory. It will lay the foundations of the theory of Mahler functions and provide a source of further research