This thesis explores several fundamental topics in mesoscopic circuitries that incorporate few electronic conduction channels. It reports a series of long-awaited experiments that establish a new state of the art.

The first experiments address the quantized character of charge in circuits. We demonstrate the charge quantization criterion, observe the predicted charge quantization scaling and a crossover toward a universal behavior as temperature is increased.

The second set of experiments addresses the unconventional quantum critical physics that arises in the multichannel Kondo model. We observe the predicted universal Kondo fixed points and validate the numerical renormalization group scaling curves. Away from the quantum critical point, we obtain a direct visualization of the development of a second-order quantum phase transition.