  A Leonard pair is a pair of diagonalizable linear transformations of a
finite-dimensional vector space, each of which acts in an irreducible
tridiagonal fashion on an eigenbasis for the other one. In the present paper we
give an elementary but comprehensive account of how the following are related:
(i) Krawtchouk polynomials; (ii) finite-dimensional irreducible modules for the
Lie algebra ${\mathfrak{sl}_2}$; (iii) a class of Leonard pairs said to have
Krawtchouk type. Along the way we obtain elementary proofs of some well-known
facts about Krawtchouk polynomials, such as the three-term recurrence, the
orthogonality, the difference equation, and the generating function. The paper
is a tutorial meant for a graduate student or a researcher unfamiliar with the
above topics.
