Ancient sources represent him as a successful student of astronomy and geography, and an early proponent of exact science. He has also been said to have introduced such astronomical instruments as the sundial and the gnomon to ancient Greece.
Cosmology and the apeiron
Anaximander's reputation is due mainly to a cosmological work, little of which remains. From the few extant fragments, 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.
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. For this, even though he had no theory of natural selection, some people consider him to be evolutionary theory's most ancient proponent.
Anaximander offered 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.
An unnamed 1911 encyclopedia has been used as a source.