  Single electron transistors (SETs) are very sensitive electrometers and they
can be used in a range of applications. In this paper we give an introduction
to the SET and present a full quantum mechanical calculation of how noise is
generated in the SET over the full frequency range, including a new formula for
the quantum current noise. The calculation agrees well with the shot noise
result in the low frequency limit, and with the Nyquist noise in the high
frequency limit. We discuss how the SET and in particular the radio-frequency
SET can be used to read out charge based qubits such as the single Cooper pair
box. We also discuss the backaction which the SET will have on the qubit. The
back action is determined by the spectral power of voltage fluctuations on the
SET island. We will mainly treat the normal state SET but many of the results
are also valid for superconducting SETs.
