Seizures are a disruption of normal brain activity present across a vast range of species, diseases, and conditions. Here we introduce a mathematical theory, Epidynamics, which provides a conceptual framework to characterize how seizures start, evolve, and terminate. We provide the first objective taxonomy of seizures based on a straightforward analysis of EEG data. Analyzing over 2000 focal-onset seizures recorded from 7 epilepsy centers on five continents, we find evidence of the predicted 16 Dynamic Classes of seizures. The theory also enables drawing a map of brain dynamics that includes most seizure classes and status epilepticus. We demonstrate that patients navigate the map during their lifetime and verify critical predictions of the theory. Epidynamics not only provides a way to stratify patients in complement to present practical classifications but also guides biophysically based mechanistic approaches and provides a language to describe the most critical features of seizure dynamics.