  Let $K$ denote a field and let $V$ denote a vector space over $K$ with finite
positive dimension. We consider an ordered pair of linear transformations
$A:V\to V$ and $A^*:V\to V$ that satisfy conditions (i), (ii) below.
  (i) There exists a basis for $V$ with respect to which the matrix
representing $A$ is irreducible tridiagonal and the matrix representing $A^*$
is diagonal.
  (ii) There exists a basis for $V$ with respect to which the matrix
representing $A$ is diagonal and the matrix representing $A^*$ is irreducible
tridiagonal.
  We call such a pair a Leonard pair on $V$. We give an overview of the theory
of Leonard pairs.
