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The Gorgon is one of the few monsters in the game to use the Death-gaze special. If your health is below 50%, a Gorgon's attack causes instant death (though Death Protection can still save you). However, this is not as dangerous as it first appears. Higher level gorgons are already very likely to deal more than half your health in a single attack, and effectively gain no benefit from their death gaze. By preying on their generally low durability, this makes them prime targets for bonus experience. Only characters with extreme durability (such as Monks or Dwarves) will even need to concern themselves with death gaze.
Where the death gaze of gorgons becomes truly dangerous is when fighting lower-level opponents. Because the gorgon has first strike, a 1st level gorgon can potentially kill a high-level adventurer if you're below half-health. The best way to deal with such gorgons is to slow them with WEYTWUT, WONAFYT or use the entanglement boon of the The Earthmother. This will disable their first strike and allow you to clean them up without risking death gaze attacks. The Assassin is also useful in this regard, since his swift hands ability ignores first strike.
If you cannot slow a gorgon, the best course of action is to try to kill them while you're at high-health to avoid their death gaze. This is especially important for users of Platemail, who likely won't even take damage from a very low-level foe but are very vulnerable to death gaze.
The Gorgon boss is Medusa, and she has 100% death gaze. This means that if you are not at full health, she will instantly kill you with her attack. She also has the Mana Burn special attack, so using the HALPMEH glyph to heal between strikes won't work. Medusa's primary weakness is that she's a relatively fragile boss, so any method of setting up a long attack chain will defeat her relatively easily. Taurog and Dracul are particularly useful for battling her, since Taurog can easily allow you to create a death protection chain to ignore her death gaze, and Dracul's blood swell, blood hunger and blood tithe boons are excellent ways to heal yourself between attacks even after your mana has been drained.