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Presumably at the birth of the Universe.
Euclid is the person credited with the invention of geometry. However the first uses of geometry are recorded to be over 5 thousand years old near the Indus Valley.
The Greeks started it This is a difficult question to answer since geometry has been around in one form or another as long as there has been written history. The Egyptians were making use of geometry to build pyramids even in prehistoric times. It was the Greeks, however who first began to rigorously study geometry and try to prove facts about it. Euclid was perhaps the most notable geometer of ancient mathematics and it was he who first axiomatized the subject (carefully defined the concepts crucial to geometry).
One main characteristic of non-Euclidean geometry is hyperbolic geometry. The other is elliptic geometry. Non-Euclidean geometry is still closely related to Euclidean geometry.
molecular geometry is bent, electron geometry is tetrahedral