Amulet of ESP
The amulet of ESP is the most common amulet on average, making up 17.5% of all randomly-generated amulets.
While worn, an amulet of ESP grants extrinsic telepathy, allowing you to see all non-mindless monsters within a radius of 8 squares around you; while blind, you can also see all non-mindless monsters on the level. Eating the amulet has a 1⁄5 chance of giving you intrinsic telepathy.
As one of two non-artifact sources of extrinsic telepathy, the amulet of ESP is one of the better amulets early on, and does not impact spellcasting like the helm of telepathy, making it more ideal for casting-focused players. In the later game, it is often replaced by the amulet of reflection or amulet of life saving; several roles have quest artifacts that provide extrinsic telepathy and can render the amulet redundant.
The amulet of ESP is one of the more straightforward amulets to informally identify, as you can use ; to far look and select a monster that you shouldn't be able to see, e.g. a pet behind a closed door, with . - the output will tell you whether you are seeing it because of telepathy, and if you have no other source, it must be coming from the amulet.
The amulet of ESP is introduced with most of the other amulets in NetHack 3.0.0.
NetHack: The Next Generation
In NetHack: The Next Generation, the home floor of the Geek quest has an amulet of ESP along with a blindfold for the purpose of viewing the text artwork created using monsters that are locked in place.
Among the defunct features in the data of SLASH'EM is The Medallion of Shifters, an artifact amulet of ESP that acted as the quest artifact for Doppelgangers before starting races and roles were made distinct in subsequent versions.
SlashTHEM adds the Geek role and its quest branch from NetHack: The Next Generation, and retains the defunct Medallion of Shifters along with much of the defunct features from SLASH'EM.