This textbook is designed to provide graduate students and other researchers in dynamical systems theory with an introduction to the ergodic theory of Lebesque spaces. The author's aim is to present a technically complete account which offers an in-depth understanding of the techniques of the field, both classical and modern. Thus, the basic structure theorems of Lebesque spaces are given in detail as well as complete accounts of the ergodic theory of a single transformation, ergodic theorems, mixing properties and entropy. Subsequent chapters extend the earlier material to the areas of joinings and representation theorems, in particular the theorems of Ornstein and Krieger. Prerequisites are a working knowledge of Lebesque measure and the topology of the real line as might be gained from the first year of a graduate course. Many exercises and examples are included to illustrate and to further cement the reader's understanding of the material. The result is a text which will furnish the reader with a sound technical background from the foundations of the subject to some of its most recent developments.