  A systematic framework is presented for the construction of hierarchies of
soliton equations. This is realised by considering scalar linear integral
equations and their representations in terms of infinite matrices, which give
rise to all (2+1)- and (1+1)-dimensional soliton hierarchies associated with
scalar differential spectral problems. The integrability characteristics for
the obtained soliton hierarchies, including Miura-type transforms,
$\tau$-functions, Lax pairs as well as soliton solutions, are also derived
within this framework.
