  Theoretical account is given of 4f-electron dynamics and multipole orders in
Pr skutterudites with particular attention to (i) mechanism of the crystalline
electric field (CEF) splitting leading to a pseudo-quartet ground state;(ii)
Kondo effect due to exchange interactions involving the pseudo-quartet;(iii)
multipole orders in the lattice of the pseudo-quartet in magnetic
field.Competition between the point-charge interaction andhybridization between
4f and conduction electrons is identified as the key for controlling the CEF
splitting. It is found that one of two pseudo-spins forming the pseudo-quartet
has a ferromagnetic exchange, while the other has an antiferromagnetic exchange
with conduction electrons. The Kondo effect is clearly seen in the resistivity
calculated by the NCA, provided the low-lying triplet above the singlet is
mainly composed of the $\Gamma_4$-type wave functions.If the weight of the
$\Gamma_5$-type is large in the triplet, the Kondo effect does not appear.This
difference caused by the nature of the triplet explains the presence of the
Kondo effect inPrFe$_4$P$_{12}$, and its absence in PrOs$_4$Sb$_{12}$.By taking
the minimal model with antiferro-quadrupole (AFQ) and ferro-type intersite
interactions for dipoles and octupoles between nearest-neighbors,the mean-field
theory reproduces the overall feature of the multiple ordered phases in
PrFe$_4$P$_{12}$. The AFQ order with the $\Gamma_3$-type symmetry is found to
be stable only as a mixture of $O_2^0$ and $O_2^2$ components.

Strongly Correlated Electrons