Drinfeld Modules This textbook offers an introduction to the theory of Drinfeld modules mathematical objects that are fundamental to modern number theory. After the first two chapters conveniently recalling prerequisites from abstract algebra and non Archimedean analysis Chapter 3 introduces Drinfeld modules and the key notions of isogenies and torsion points. Over the next four chapters Drinfeld modules are studied in settings of various fields of arithmetic importance culminating in the case of global fields. Throughout numerous number theoretic applications are discussed and the analogies between classical and function field arithmetic are emphasized. Drinfeld Modules guides readers from the basics to research topics in function field arithmetic assuming only familiarity with graduate level abstract algebra as prerequisite. With exercises of varying difficulty included in each section the book is designed to be used as the primary textbook for a graduate course on the topic and may also provide a supplementary reference for courses in algebraic number theory elliptic curves and related fields. Furthermore researchers in algebra and number theory will appreciate it as a self contained reference on the topic. Preface Acknowledgements Notation and Conventions Chapter 1. Algebraic Preliminaries Chapter 2. Non Archimedean Fields Chapter 3. Basic Properties of Drinfeld Modules Chapter 4. Drinfeld Modules over Finite Fields Chapter 5. Analytic Theory of Drinfeld Modules Chapter 6. Drinfeld Modules over Local Fields Chapter 7. Drinfeld Modules over Global Fields Appendix A. Drinfeld modules for general function rings Appendix B. Notes on exercises Bibliography Index.