In the philosophy of Immanuel Kant, a noumenon or thing in itself (German Ding an sich) is an unknowable, undescribable reality that, in some way, lies "behind" observed phenomena. The etymology of the word ultimately reflects the Greek nous (mind).
Some writers also refer to noumena (the plural form), though the very notion of individuating items in "the noumenal world" seems problematic, since the very notions of number and individuality appear among the categories of understanding -- so that individuality itself is a noumenon. "Phenomenon" serves as a (contrasting) technical term in Kant's philosophy, meaning the world as experienced.
Explaining the relationship between the noumenal and phenomenal worlds forms one of the most difficult problems for Kant's philosophy. On Kant's view as expressed in his Critique of Pure Reason, reality is structured by so-called "concepts of the understanding", or innate categories that the mind brings to make sense of raw unstructured experience. Since these categories include causality and number, it becomes problematic to say that "many" noumena exist that individually "cause" us to have perceptions of phenomena. But if the noumenal does not cause the phenomenal, then what is the relationship? The answer is that the noumenal and phenomenal coexist simultaneously; we cannot say that either causes the other.
It can be said that on Kant's view the noumenal is radically unknowable. Whatever concept we might want to use to categorize some noumenon or noumena, that is only a way of categorizing phenomena, so that the act of knowing a noumenon must itself be defined by a noumenon, a situation that is unresolvable.
See also