  We first give an overview of the shell-correction method which was developed
by V. M. Strutinsky as a practicable and efficient approximation to the general
selfconsistent theory of finite fermion systems suggested by A. B. Migdal and
collaborators. Then we present in more detail a semiclassical theory of shell
effects, also developed by Strutinsky following original ideas of M.
Gutzwiller. We emphasize, in particular, the influence of orbit bifurcations on
shell structure. We first give a short overview of semiclassical trace
formulae, which connect the shell oscillations of a quantum system with a sum
over periodic orbits of the corresponding classical system, in what is usually
called the "periodic orbit theory". We then present a case study in which the
gross features of a typical double-humped nuclear fission barrier, including
the effects of mass asymmetry, can be obtained in terms of the shortest
periodic orbits of a cavity model with realistic deformations relevant for
nuclear fission. Next we investigate shell structures in a spheroidal cavity
model which is integrable and allows for far-going analytical computation. We
show, in particular, how period-doubling bifurcations are closely connected to
the existence of the so-called "superdeformed" energy minimum which corresponds
to the fission isomer of actinide nuclei. Finally, we present a general class
of radial power-law potentials which approximate well the shape of a
Woods-Saxon potential in the bound region, give analytical trace formulae for
it and discuss various limits (including the harmonic oscillator and the
spherical box potentials).
