In this thesis, were studied three nanoscopic quantum dot (QD) systems. First, the so-called Kondo cloud was analyzed, the extension of the conduction band spin screening of a magnetic impurity embedded in a metallic matrix and represented, in our case, by a QD. The Kondo cloud properties were obtained studying the way in which the local density of states of the metallic matrix sites reflects the Kondo resonance and also through the spin-spin correlations between the QD and the conduction band spins. It was possible to find a good agreement between the Kondo cloud extensions obtained using both methods. The second system consists of three aligned QDs with the central QD connected to two metallic leads. The operation of this system as a quantum gate was studied, which depends on the central QD charge. A time dependent study of the system properties and, in particular, of the lateral QDs spin correlation was developed. We showed that the Kondo effect, reflected in the conductance, could be a fundamental tool to measure the information contained in the quantum gate state. The first two systems were treated using the Slave Bosons Mean Field Approximation method. Finally, we studied the thermoelectric transport of a two QD system when one of them is connected to two onedimensional leads. The system was analyzed in the linear and nonlinear response to an external applied potential, always in the Coulomb blockade regime. It was found that the presence of Fano resonances and a Van-Hove singularity in the one-dimensional lead density of states near the Fermi level are fundamental ingredients to enhance thermoelectric efficiency. The many-body problem was treated in the Hubbard III approximation, which is a correct approach to study the transport properties for T greater than TK, where TK is the Kondo temperature.