Kernel
Euclid wrote the Elements at Alexandria — thirteen books that organize Greek geometry as a deductive system flowing from five postulates. It is the single most successful textbook ever produced; it remains a working pedagogy for two millennia and is the formal model for Newton's Principia and Spinoza's Ethics, both of which are structured "more geometrico" (in the geometrical manner).
Contribution
The axiomatic method as it is still taught. The Pythagorean theorem in its rigorous form. Proofs of irrationality. The infinity of primes. Algorithmic computation (the Euclidean algorithm). The very notion that mathematics consists of theorems derived from clearly stated premises.
Lineage
The Elements travels: Greek → Arabic (Baghdad, 9th century) → Latin (Toledo, 12th century) → printed editions all across Europe from 1482 onwards. Newton studied it; so did Spinoza; so did Lincoln (who taught himself by reading it). Modern computer-assisted proof systems still cite it as the canonical first axiom system.
Civilization-scale significance
The format Euclid invented — definition, postulate, theorem, proof — is so successful that we forget it was invented. It is the single most exported intellectual artifact of antiquity.