  This pedagogical article is aimed to the beginning graduate students
interested in broad field of frustrated magnetism. We introduce and present
some of the exact results obtained in Kitaev model. The Kitaev model embodies
an unusual two spin interactions yet exactly solvable model in two dimension.
This exact solvability renders it to realize many emergent many body phenomena
such as $Z_2$ gauge field, spin liquid states, spin fractionalization,
topological order exactly. First we present the exact solution of Kitaev model
using Majorana fermionisation and elaborate in detail the $Z_2$ gauge
structure. Following this we discuss exact calculation of magnetization,
spin-spin correlation function establishing its spin-liquid character. Spin
fractionalization and de-confinement of Majorana fermion is explained in
detail. Existence of long range multi-spin correlation function and topological
degeneracy are discussed to elucidate the entangled and topological nature of
any eigenstate. Some elementary questionnaires are provided in appropriate
places for assimilation of the technical details.
