In this Thesis, we develop an effective low energy Fermi liquid formalism to describe the electron dynamics in the strongly interacting quantum RC circuit. This device is composed of a quantum dot connected to an electron reservoir by a quantum point contact. The dot is coupled capacitively to a top metallic gate. Direct current is forbidden and electron transport can be observed if the quantum dot is driven by a time dependent gate potential. Theoretical and experimental studies confirmed the analogy to a classical RC circuit and showed a violation of Kirchhoff's laws for phase-coherent transport: the charge relaxation resistance of the quantum RC circuit is universally quantized to R_q = h/2e^2 , regardless of the quantum point contact transmission, in striking contrast to direct transport measurements. We consider Coulomb blockade regimes caused by strong electronic interactions on the dot. For both spinless and spinful electrons, we show electron dynamics to be effectively non-interacting at low temperature. We derive a generalized Korringa-Shiba relation, predicting universal quantization for the charge relaxation resistance even in the presence of strong interactions on the dot. We also study non-universal behaviors of R_q for spinful electrons in the presence of a magnetic field. We focus on the Kondo regime and show the emergence of a giant peak for R q caused by the destruction of the Kondo singlet. We extend our approach to the SU(4) symmetric case, relevant in the case of further orbital degeneracy on the dot. The analytical methods developed in this work are applied to obtain the exact expression of the SU(4) Kondo temperature.
