Reciprocal Space
Reciprocal space (also called "k-space") is the space in which the Fourier transform of a spatial function is represented (similarly the frequency domain is the space in which the Fourier transform of a time dependent function is represented). A Fourier transform takes us from "real space" to reciprocal space or vice versa.
A reciprocal lattice is a periodic set of points in this space, and contains the points that compose the Fourier transform of a periodic spatial lattice. The Brillouin zone is a volume within this space that contain all the unique k-vectors that represent the periodicity of classical or quantum waves allowed in a periodic structure.
Read more about this topic: Reciprocal Lattice
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—Storm Jameson (1891–1986)