  We present spectroscopic measurements of the Autler-Townes doublet and the
sidebands of the Mollow triplet in a driven superconducting qubit. The ground
to first excited state transition of the qubit is strongly pumped while the
resulting dressed qubit spectrum is probed with a weak tone. The corresponding
transitions are detected using dispersive read-out of the qubit coupled
off-resonantly to a microwave transmission line resonator. The observed
frequencies of the Autler-Townes and Mollow spectral lines are in good
agreement with a dispersive Jaynes-Cummings model taking into account higher
excited qubit states and dispersive level shifts due to off-resonant drives.
