  While the composite fermion picture is so effective as to describe the
excitation spectra including the spin wave for Laughlin's quantum liquid, ``how
heavy and how strongly-interacting" remains a formidable question for the
composite fermions, to which this article first addresses. The effective mass
(purely interaction originated) defined from the excitation spectrum and
obtained for various even- as well as odd-fractions exhibits a curious,
step-like filling dependence basically determined by the number of flux quanta
attached to each fermion, where the non-monotonic behaviour indicates a strong
effect of gauge-field fluctuations. The excitation spectrum fits a Fermi
liquid, but again a large effect of inter-composite fermion interaction appears
as anomalous Landau's parameters. We have then moved on to see how the
introduction of three-dimensionality (where the shape of the Fermi surface
becomes relevant) affects the interacting electron system, and propose the
magnetic-field induced SDW in three-dimensional systems. This should be a good
candidate, in entirely realistic magnetic fields, for the integer QHE recently
predicted by Koshino et al to occur in 3D on the fractal energy spectrum
similar to Hofstadter's. The mechanism for the field-induced phase is an effect
of interaction in Landau's quantisation on incompletely-nested (i.e.,
multiply-connected) Fermi surfaces, so the interplay of many-body physics and
the magnetic quantisation on various Fermi surfaces may provide an interesting
future avenue for 3D systems.
