He was born in 325 BC and died in 265 BC. (Some sources suggest he died in 275 BC.)
Euclid worked as a mathematician in Alexandria during the reign of Ptolemy 1. Little is known of his life.

The textbook Elements was so popular it was a major work for over 2000 years. It contained much of the knowledge of that time in regard to geometry and arithmetic. The Elements consists of 13 books of increasing complexity. Euclid's reasoning moved from the basic definitions of geometric concepts such as a circle, point, line etc. He then built axioms and postulates for more complex theorems which in turn were used to develop even more complex theorems.

The Elements presented the theories of the time in one coherent and logical framework and is now referred to as Euclidean geometry or in earlier times as 'the geometry'.

Euclid's proof that for a right-angled triangle the area of a semicircle along the hypotenuse is equal to the sum of the areas of the semicircles on the other two sides. This is a further development of Pythagoras's theorem.

He determined that the square root of two is irrational.

He is also attributed with determining that the number of primes is infinite

Later in the 19th century, Carl Frederich Gauss and particularly Janos Bolyai determined there were non-euclidean geometries. These were further explored by Riemann, Lobachevsky, and Poincaré.

http://www.obkb.com/dcljr/euclid.html