  The aim in this paper is to give expressions for modular linear differential
operators of any order. In particular, we show that they can all be described
in terms of Rankin-Cohen brackets and a modified Rankin-Cohen bracket found by
Kaneko and Koike. We also give more uniform descriptions of MLDOs in terms of
canonically defined higher Serre derivatives and an extension of Rankin-Cohen
brackets, as well as in terms of quasimodular forms and almost holomorphic
modular forms. The last of these descriptions involves the holomorphic
projection map. The paper also includes some general results on the theory of
quasimodular forms on both cocompact and non-cocompact subgroups of
$SL_2(\mathbb{R})$, as well as a slight sharpening of a theorem of Martin and
Royer on Rankin-Cohen brackets of quasimodular forms
