"Small Dynamic Complexity Classes" was awarded the E.W. Beth Dissertation Prize 2016 for outstanding dissertations in the fields of logic, language, and information. The thesis studies the foundations of query re-evaluation after modifying a database. It explores the structure of small dynamic descriptive complexity classes and provides new methods for proving lower bounds in this dynamic context. One of the contributions to the former aspect helped to confirm the conjecture by Patnaik and Immerman (1997) that reachability can be maintained by first-order update formulas.