Euclid's work, Elements of Geometry, is considered the most important text of Greek times. This work comes in thirteen books; although from various sources, were organized by him. He is believed to have studied and taught at the Museum of Alexandria. More than two thousand years later, only the Bible has more translations and editions than it.

Euclid came up with the idea of postulates. Apart from this, he attempted to define his concepts, but were not actually definitions and more like explanations. He also visualized and explored the idea of parallel lines, the foundation of many of his propositions.

His basic postulates are that a straight line can be drawn from any one point to another, a finite straight line can be produced continuously in a line, a circle can have any center or distance, and that all right angles are equal. The fifth, the Parallel Postulate, has intrigued mathematicians. It states that if a straight line falls on two straight lines such that the interior angles on the same side are less than a right angle, then the two straight lines will meet on that side.

Many of his proofs are based on geometric reasoning from diagrams. Among his propositions, many are on elementary plane geometry. These include the properties of congruent triangles, the equality of base angles of an isosceles triangle, construction of perpendiculars, properties of angles within a pair of parallel lines, the sum of the three interior angles of a triangle is equal to two right angles, as well as proofs of the Pythagorean Theorem.

He also proposed proving algebraic rules geometrically, including that of the expansion of (a + b)². Construction of circles, solid geometry and similarity are other fields that he dealt with.