Anaximander was born in Miletus around the year 611 BCE. The Milesian school of philosophy had its roots in Anaximander's older associate: Thales. Anaximander was surely influenced by Thales, but did not follow closely in his footsteps. In fact, Anaximander's ideas seem a blatant contrast and a reaction to Thales' philosophy.
What we know about Anaximander is a more clear than what we know of Thales. Fragments of a prose work written by Anaximander in the Ionian dialect still remain today, whereas we having nothing but second-hand testimony from Thales. From the fragments we still have from Anaximander, it is clear that Anaximander rejected Thales' claim that the primary substance is Water, from which all thing rise. Anaximander claimed that the original and primary substance from which all things are born and pass into is Infinite and Boundless. Anaximander thought that the world is composed of dynamic opposites, which are 'separated out' from the Formless and Infinite primary mass of the Cosmos. Anaximander felt that Thales put too much emphasis on the 'wet', as opposed to the 'dry.' Likewise, he would have likely said that his pupil, Anaximenes, erred in putting too much emphasis on Air. This idea of the natural ordering of dynamically opposed forces seems to pervade Anaximander's philosophical activity. Anaximander's views of other problems, such as justice follow this pattern, as well: 'Things give satisfaction and reparation to one another for their injustice, as is appointed according to the ordering of time.'
As Thales had done before him, Anaximander constructed a 'scientific' view of the Earth. He rejected Thales' model of the Earth as a disc that floated upon water. Anaximander claimed the Earth came into its being by the 'separating out' of opposites. He felt that there must not be anything to make the Earth fall in one direction or the other, because he felt that there is neither an 'absolute' up nor down, so instead he proposed the Earth to be a 'short cylinder,' swinging freely in space.
Anaximander's views on the origin of mankind seem to give some weight to Thales' philosophy, for Anaximander claimed that living beings emerged from the sea and adapted to the new environment, giving them new forms.
Why should we care about these ancient philosophers, and cosmologies that aren't scientifically accurate? Well, if you want to take the opinion of a classical philologist, try reading the essay "Philosophy in the Tragic Age of the Greeks," written by Friedrich Nietzsche. It discusees the unrivalled greatness of these men and how they serve as archetypes of philosophical thought until this very idea. Nietzsche's eternal recurrence was not even totally his own, for already had its birth in Pre-socratic thought.
Also, since people shared the same name alot in ancient Greece it is important to give their full name like "Anaximander of Miletus" instead of just "Anaximander," when you are talking about them formally, or else it would just be a big free-for-all then wouldn't it? I decided to do this for clarity. Is clarity not vital when constructing an information database. Its like when you refer to David Hume - you use the full name and not just David or Hume, because there are many people who share those names.