  Magnetic and other unconventional electronic orders are discussed for heavy
electrons. In addition to the ordinary Kondo lattice, we consider non-Kramers
systems taking the two-channel Kondo lattice, and another lattice that consists
of a singlet-triplet f2 configuration. The latter gives a scalar order with
staggered sublattices of crystalline-electric-field (CEF) and Kondo singlets,
which accounts for the observed order in PrFe4P12. In the two-channel Kondo
lattice, an odd-frequency pairing is realized that becomes degenerate at
half-filling with a composite order involving both localized and conduction
electrons. The degeneracy is interpreted in terms of a hidden SO(5) symmetry.
For the ordinary Kondo lattice with exchange interaction J, we take insulating
ground states as reference. The metallic states are approached by infinitesimal
doping of carriers either from the Kondo insulator or from the
antiferromagnetic insulator. By adding intersite exchange we find that location
of the band extremum of the heavy band depends on the value of J. The change of
J gives topological change of the Fermi surface, which corresponds to a
generalized version of the Lifshitz transition, and occurs separately from the
quantum critical point of the antiferromagnetic order.
