The Gorgon is one of the special races in Desktop Dungeons. It is unlocked by clearing the Snake Pit with a Monk. Gorgons are known for their death gaze, which petrifies anyone under a given amount of health. They also are physically durable and can poison foes.
Once the enemy's HP is below your Death Gaze percentage, attacking them with melee will cause your damage to be exactly the HP required to instantly kill them. The Death Gaze percentage and resulting damage is unaffected by resistances. This damage may be lower than your actual current Attack, so keep this in mind for increasing the Damage score in Ranked games—though this often won't matter so much with the Gorgon's low Damage Bonus.
You do not have First Strike, unlike enemy Gorgons. The petrification on kill counts towards The Earthmother's reward, but it does not count towards any Score rewards. However, since all enemies you kill will be petrified, you may have to use ENDISWAL a lot: plan for this extra mana cost requirement, and note that the Earthmother will punish you for using it if you choose her. And remember that the Gorgon only starts with Physical Resistance: Dragonspawn, Warlocks and Wraiths will still do full damage to you.
Since the Gorgon starts with an extra Glyph, Death Gaze caps at 40% when all Glyphs on the map have been converted; if Glyphs are available from shops, it can go higher. This means that you can kill a boss which would otherwise outlast you by taking it down to less than 40% health and then converting all of your glyphs; this can be especially helpful when you have to face bosses that are immune to Poison, as in the Crypt.
Binlor Ironshield is easy to gain piety for thanks to ENDISWAL, and the Mining boon is a bit more useful for gorgons than most other classes, but his other boons aren't worth the trouble. The Earthmother isn't an option thanks to your ENDISWAL, and Glowing Guardian won't support your poisonous attack. Probably the best choice of god (aside from the universally-helpful Pactmaker) is Jehora Jeheyu, since destroying walls grants a small amount of piety.
Mystera Annur is a fabulous choice for the Gorgon, since having an Attack of 1 won't prevent Poison from being applied - nor will it prevent Death Gaze from functioning. As long as you can reduce an enemy's health to below your Death Gaze threshold using BURNDAYRAZ, a single attack will kill it regardless. Note, however, that you need to convert Glyphs to increase the effectiveness of Death Gaze, while doing so will offend Mystera; converting as many Glyphs as possible before worshiping her is preferred.