Anaximander was born in 609-610 B.C. and was a citizen of Miletus and a companion or pupil of Thales. Thought little is known of his life and work, ancient sources represent him as a successful student of astronomy and geography, and has been said to have introduced such astronomical instruments as the sundial and the gnomon to ancient Greece.
From the few fragments of his work which survive, we learn that he believed the beginning or first principle (arche, a word first found in Anaximander's writings, and which he probably invented) is an endless, unlimited mass (apeiron), subject to neither old age nor decay, which perpetually yields fresh materials from which everything which we can perceive is derived. He never defined this principle precisely, and it has generally (e.g. by Aristotle and Augustine) been understood as a sort of primal chaos. It embraced the opposites of hot and cold, wet and dry, and directed the movement of things, by which there grew up all of the host of shapes and differences which are found in the world.
Anaximander offers up the theory of the apeiron in direct response to the earlier theory of Thales, who had claimed that the primary substance was water. Anaximander reasons that water cannot embrace all of the opposites found in nature -- for example, water can only be wet, never dry -- and therefore, it can't be the one primary substance. Nor could any of the other candidates, so Anaximander postulated the apeiron as a substance though it could not be perceived directly could explain the opposites which he could clearly see around him.
Anaximander also believed in a progression of species from one to another, and though he had no notion of natural selection, some people consider him to be evolutionary theory's most ancient proponent.
From the unnamed 1911 encyclopedia
ANAXIMANDER, the second of the physical philosophers of Ionia, was a citizen of Miletus and a companion or pupil of Thales. Little is known of his life. Aelian makes him the leader of the Milesian colony to Amphipolis, and hence some have inferred that he was a prominent citizen. The computations of Apollodorus have fixed his birth in 611, and his death shortly after 547 B.C. Tradition, probably correct in its general estimate, represents him as a successful student of astronomy and geography, and as one of the pioneers of exact science among the Greeks. He taught, if he did not discover, the obliquity of the ecliptic, is said to have introduced into Greece the gnomon (for determining the solstices) and the sundial, and to have invented some kind of geographical map. But his reputation is due mainly to his work on nature, few words of which remain. From these fragments we learn that the beginning or first principle (arche, a word which, it is said, he was the first to use) was an endless, unlimited mass (apeiron), subject to neither old age nor decay, and perpetually yielding fresh materials for the series of beings which issued from it. He never defined this principle precisely, and it has generally (e.g. by Aristotle and Augustine) been understood as a sort of primal chaos. It embraced everything, and directed the movement of things, by which there grew up a host of shapes and differences. Out of the vague and limitless body there sprung a central mass,--this earth of ours, cylindrical in shape, poised equidistant from surrounding orbs of fire, which had originally clung to it like the bark round a tree, until their continuity was severed, and they parted into several wheel-shaped and fire-filled bubbles of air. Man himself and the animals had come into being by like transmutations. Mankind was supposed by Anaximander to have sprung from some other species of animals, probably aquatic. But as the measureless and endless had been the prime cause of the motion into separate existences and individual forms, so also, according to the just award of destiny, these forms would at an appointed season suffer the vengeance due to their earlier act of separation, and return into the vague immensity whence they had issued. Thus the world, and all definite existences contained in it, would lose their independence and disappear in the "indeterminate." The blazing orbs, which have drawn off from the cold earth and water, are the temporary gods of the world, clustering round the earth, which, to the ancient thinker, is the central figure.