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Nymphs are a species of female spirits originating from Greco-Roman mythology and one of Western culture's earliest forms of monstergirls. Distantly related to the gods, but far less powerful, nymphs are spirits tied to various aspects of nature - their most common subdivisions being the famous Dryads (tree spirits) and less famous but still somewhat recognizable Niads (spring & river spirits) and Oceanids (ocean spirits), but there are many, many others, including Oreads (mountain spirits), Limoniads (meadow spirits), Limniads (lake/marsh/swamp spirits), and Napaea (valley & glen spirits). Nymphs are particularly known for being pursued by amorous menfolk, from humans to satyrs to gods.
Though the name is taken from Western culture, the concept of "beautiful female spirit" is pretty universal, and beings akin to nymphs show up in almost every polytheistic mythos.
Despite this, nymphs have never really enjoyed a lot of attention in /tg/ related works, simply because the concept is both extraordinarily broad ("nymph" can, realistically, refer to any beautiful female fey, from an elf to a mermaid) and surprisingly weak - a nymph is basically just a super-beautiful "non-human, but doesn't look it" woman.
Dungeons & Dragons has traditionally included nymphs over multiple editions, but they're not really acknowledged much, simply because they're obvious fapbait and, unlike the succubus or lamia, they don't really have anything to distinguish them beyond that. Your D&D nymph is basically a high level, max charisma, female elf sorceress (Enchanter) multiclassed with duid with one unique ability: if you see her naked, you gotta make a save to avoid dying, and then another save to not go blind if you live. Apparently because they're "so beautiful". That's really it. The 2e monster manual doesn't even detail how they procreate.
In the World Axis cosmology for Dungeons & Dragons 4th Edition, nymphs didn't appear until the 3rd Monster Manual, but received quite the fluff update. Daughters of the four seasons and fathered by the four winds, the nymphs are fickle, tempestuous creatures who consider life a grand game in which their having fun is the only thing that matters - and where mortals are intriguing, but ultimately replaceable, toys. Beautiful but untrustworthy, they are divided into five categories; Spring, Summer, Autumn, Winter and Wood.
Spring Nymphs fixate on the way that life is always replenished and enhanced by spring. They are the most hedonistic of the nymphs, and live to amuse themselves and their infinite hunger for sensation, reveling in manipulating mortals to become their playmates. Their kiss can sear a mind with pure passion, and their song can ensnare the weak-willed, rendering them prey to the hypnotic allure of their sweet personal scent.
Summer Nymphs are the oldest and wisest of their ilk, and live in contemplative wonder of the mysteries of eternity, but have learned no compassion with their wisdom. They amuse themselves with a strange and enigmatic game, alternatively aiding and attacking the denizens of the mortal realm or the Feywild alike as part of their own mysterious goals. Their vision can burn with the brilliance of the midsummer sun, and their touch scramble a mind with an influx of alien wisdom. If truly pressed, they can summon violent summer storms to defend themselves and their followers - beasts and plants and lesser fey.
Autumn Nymphs are obsessed with stories, and will readily trade them with mortals; in many ways, they are the most docile of their sisters, but woe betide the bargainer who refuses to live up to their end of the deal and share a story in return! They wreak a subtle vengeance, deluging their victim with dark and hidden secrets, overwhelming their minds with knowledge they cannot bear and ruining their lives. Ironically, autumn nymphs are the most melancholic of their kind, for they see life in perpetual decline.
Winter Nymphs are preachers of the philosphy that only the strongest survive, hunting monsters and humanoids alike to take their heads as trophies in bloody raids.
Wood Nymphs are autumn nymphs who have succumbed to their melancholy and begun to replace it with rage, being consumed by an urge to battle for nature's survival that causes them to begin merging with a single tree. This path can ultimately cause them to transform into either hamadryads or dryads.