"Common" Greek mythology monsters would be for an example the Minotaur, Medusa, Chimeras, Hydra, Charybdis and Scylla, Harpies, Cyklops and two-headed snakes.
Examples of creatures that are certainly not natural, but mayhaps not monsters either, are Pegasus, Centaurs, Satyrs, Nymphs and Mermaids.
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Some are:
Chimera, Cyclopes, Echidna, Giants, Gorgons, Harpies, Nymphs, Centaurs, Charybdis, Ichthyocentaurs, Manticore, Minotaur, Hydra, Scylla, Arion, Ballius and Xanthus, Calydonian boar, Nemean lion, Phoenix, Sphinx, and Ladon. These are all the ones I can think of off the top of my head. :)Greek mythology monsters were usually scary, like the Minotaur, half man-half bull, the hell hounds, humongous dogs with usually multiple heads, and cyclops, extremely tall creatures that looked like humans, but had one eye, were stronger, but were usually stupid. But the good guy creatures weren't that scary, like satyrs, half goat-half man.
The Minotaur, Scylla, Charybdis, Cyclops, Centaur, Cerberus, Hippocampi, The Furies (The Kindly Ones), Gorgons, Echidne, The Hundred-Handed Ones, Hydra, Chimera, etc.
Pegasus, centaurs, satyrs, harpies, gorgons (such as Medusa and her two sisters), unicorns, minotaurs, Phoenix birds, Cyclops, and many others.
centaur, minotaur, pegasus, dryad, drakon, giants, hippocampi, telekhines, mermaids, and hellhounds.
In Greek mythology, Medusa is often depicted as a monstrous woman with snakes for hair and a gaze that turns people to stone.
No one for sure knows what anyone from the greek mythology stories look like for sure, but it is said that telemachus looked alot like his father odysseus
Hermes tricked the sirens into eating themself by painting them to look like humans why they were sleeping.
Pterippus. Related to hippogryph, as they look sometimes look more horse like than not.Pegasus was the name of the winged-horse of Greek mythology; it is commonly used to refer to all winged-horses despite being a proper name.
There are many gods and goddesses who live on Mount Olympus so it must be very nice.