Introduction 1. Basic Theory of Zariski Surfaces 2. Links with Differential Equations in Characteristic p > 0 3. The Divisor Classes of the Surface zpn = G(x,y) 4. Picard Groups of Generic Zariski Surfaces 5. The Divisor Classes of zp = G(x,y): A Programmable Problem 6. Families of Zariski Surfaces 7. Unirationality of Enriques Surfaces in Characteristic 2 8. Applications of the de Rham-Witt Complex and of Dominoes to Zariski Surfaces 9. Picard and Brauer Groups of Zariski Surfaces 10. A Counterexample to Zariski's Problem and an Example of a Surface with Nonreduced Picard Scheme
