  Motivated by recent experiments, in which the Kondo effect has been observed
for the first time in a double quantum-dot structure, we study electron
transport through a system consisting of two ultrasmall, capacitively-coupled
dots with large level spacing and charging energy. Due to strong interdot
Coulomb correlations, the Kondo effect has two possible sources, the spin and
orbital degeneracies, and it is maximized when both occur simultaneously. The
large number of tunable parameters allows a range of manipulations of the Kondo
physics -- in particular, the Kondo effect in each dot is sensitive to changes
in the state of the other dot. For a thorough account of the system dynamics,
the linear and nonlinear conductance is calculated in perturbative and
non-perturbative approaches. In addition, the temperature dependence of the
resonant peak heights is evaluated in the framework of a renormalization group
analysis.
