In abstract algebra, a normal subgroup is a subgroup which is invariant under conjugation by members of the group of which it is a part. In other words, a subgroup H of a group G is normal in G if and only if aH = Ha for all a in G (see coset). Normal subgroups (and only normal subgroups) can be used to construct quotient groups from a given group.
Évariste Galois was the first to realize the importance of the existence of normal subgroups.
Read more about Normal Subgroup: Definitions, Examples, Properties, Normal Subgroups and Homomorphisms
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“Our normal waking consciousness, rational consciousness as we call it, is but one special type of consciousness, whilst all about it, parted from it by the filmiest of screens, there lie potential forms of consciousness entirely different.”
—William James (1842–1910)