  The occurrence of incompressible quantum fluid states of a two dimensional
system is a result of electron--electron interactions in a highly degenerate
fractionally filled Landau level. Novel quasiparticles (QP's) called composite
Fermions (CF's) have allowed a simple single particle description of the most
prominent incompressible states. Residual interactions among these QP's are
investigated. These interactions determine the type of "daughter states" that
can occur at the next generation. We demonstrate that at certain values of the
QP filling factor nu_QP, Laughlin correlations among the QP's give rise to
states of the standard CF hierarchy. At other values of nu_QP pairing of QP's
is found leading to a novel hierarchy of incompressible states.
