"On those stepping into rivers staying the same other and other waters flow." (DK22B12)Heraclitus espoused the theory of universal flux, "the coincidence of opposites," and the centrality of fire. Diogenes Laertius says that Heraclitus won the honorary title of king of the Ionians and wrote a book that he deposited at the temple of Artemis at Ephesus. (Over 100 fragments survive.) The book was divided into sections on cosmology, politics, and theology.
Heraclitus is not connected with one of the other Pre-Socratic schools. He believed that everything is fire in some modified form, that everything is always changing or in flux, and this "entails the coincidence of opposites," meaning that things are both the same and opposite each other at the same time.
Heraclitus is the first known to use the word kosmos for world order, which he says ever was and ever will be, not created by god or man.
Heraclitus is called a monist (because he believes fire is the underlying principle) and an elitist (he believes most people are stupid). Although Heraclitus does not seem to have been in a school, he may have influenced Parmenides, Empedocles, Democritus, Plato, and the Stoics.
Graham, Daniel W., "Heraclitus", The Stanford Encyclopedia of Philosophy (Spring 2007 Edition), Edward N. Zalta (ed.), URL = <http://plato.stanford.edu/archives/spr2007/entries/heraclitus/>.