  This manuscript contains a small portion of the algebraic theory of
orthogonal polynomials developed by Maroni and their applicability to the study
and characterization of the classical families, namely Hermite, Laguerre,
Jacobi, and Bessel polynomials. It is presented a cyclical proof of some of the
most relevant characterizations, particularly those due to Al-Salam and
Chihara, Bochner, Hahn, Maroni, and McCarthy. Two apparently new
characterizations are also added. Moreover, it is proved through an equivalence
relation that, up to constant factors and affine changes of variables, the four
families of polynomials named above are the only families of classical
orthogonal polynomials.
