Short answers, pulled from the story.
Euclid wrote the textbook called Elements in the ancient Greek city of Alexandria. This book organized geometric knowledge into a logical system where every statement followed from a small set of starting assumptions.
János Bolyai and Nikolai Ivanovich Lobachevsky independently published their work on 1830. Their discovery proved that the parallel postulate could never be derived from the other four axioms.
Ludwig Schläfli performed this work in relative obscurity, and his findings were published fully only after his death in 1901. The research remained largely unnoticed until H.S.M. Coxeter rediscovered and documented it in 1948.
Albert Einstein's theory of general relativity showed that physical space itself is not Euclidean because gravity causes deviations from Euclidean rules. A solar eclipse in 1919 provided evidence for this prediction when starlight bent around the Sun.
David Hilbert developed a set of independent axioms designed to make Euclidean geometry rigorous and avoid hidden assumptions. Moritz Pasch began improving axiomatic systems in 1882 before Hilbert's work.