  In this work we use the Slave Boson Mean Field Approximation at finite U to
study the effects of spin-spin correlations in the transport properties of two
quantum dots coupled in series to metallic leads. Different quantum regimes of
this system are studied in a wide range of parameter space. The main aspects
related to the interplay between the half-filling Kondo effect and the
antiferromagnetic correlation between the quantum dots are reviewed. Slave
boson results for conductance, local density of states in the quantum dots, and
the renormalized energy parameters, are presented. As a different approach to
the Kondo physics in a double dot system, the Kondo cloud extension inside the
metallic leads is calculated and its dependence with the inter-dot coupling is
analyzed. In addition, the cloud extension permits the calculation of the Kondo
temperature of the double quantum dot. This result is very similar to the
corresponding critical temperature $T_c$, as a function of the parameters of
the system, as obtained by using the finite temperature extension of the Slave
Boson Mean Field Approximation.
