Short answers, pulled from the story.
Euclid was an ancient Greek mathematician active as a geometer and logician around 300 BC. He is called the father of geometry and is chiefly known for the Elements, a thirteen-book treatise that established the foundations of geometry. He is generally ranked with Archimedes and Apollonius of Perga among the greatest mathematicians of antiquity.
Euclid is generally accepted to have lived around 300 BC and to have spent his career in Alexandria. Proclus placed him after Plato's followers and before Archimedes, during the rule of Ptolemy I. His exact birthdate and birthplace are unknown, with some scholars estimating his birth around 330 or 325 BC.
The Elements is Euclid's thirteen-book treatise covering plane geometry in books 1 to 6, basic number theory in books 7 to 10, and solid geometry in books 11 to 13. It deduces theorems from a small set of axioms, including five postulates and five common notions in Book 1. It contains the earliest surviving proof of the Pythagorean theorem and the proof that there are infinitely many prime numbers.
Euclid the mathematician was conflated with Euclid of Megara, an earlier philosopher and pupil of Socrates, in now-lost Byzantine sources. The Roman writer Valerius Maximus mistakenly substituted Euclid's name for Eudoxus, and scholars such as Theodore Metochites around 1300 explicitly merged the two men. The error spread through printed editions until Peter Ramus reevaluated and disproved related claims.
Besides the Elements, at least five of Euclid's works survive, including the Optics on perspective, the Data, the Phaenomena on spherical astronomy, Catoptrics, and On Divisions. Four further works are credibly attributed to him but lost, including the Conics, the Pseudaria, the Porisms, and the Surface Loci.
According to Proclus, when Ptolemy asked Euclid if there was a quicker path to learning geometry than reading the Elements, Euclid replied that there is no royal road to geometry. The anecdote is questioned because a very similar exchange between Menaechmus and Alexander the Great was recorded by Stobaeus.
The Elements is often considered, after the Bible, the most frequently translated, published, and studied book in the history of the Western world. It was the dominant mathematical textbook in the Medieval Arab and Latin worlds, and its system is now called Euclidean geometry. Its first English edition was published in 1570 by Henry Billingsley and John Dee.