Basic Structures of Function Field Arithmetic

The arithmetic of function fields over finite fields has been an area of extensive research since the mid-1970s with interesting results being obtained. This text offers an introduction to basic concepts such as Drinfeld modules, T-modules, shtuka, exponentiation of ideals and characteristic p L-functions and Gamma-functions in all their various manifestations. Insight from classical number theory, differential equations/algebra and algebraic geometry is presented when needed. Unsolved problems are posed to the reader and a comprehensive list of references is included.