We have recorded laser excitation spectra of transitions from the ground X-1 Sigma(+) state of gaseous gold fluoride (AuF) into three excited electronic states in the visible region. We prepared the sample in a dc electric discharge by flowing a dilute mixture of SF6 in argon through a hollow gold cathode. Two of these electronic states give rise to the previously reported yellow bands of the molecule, for which a rotational analysis is given here for the first time. We have analyzed the (0,0), (1,1), (0,1), and (1,2) bands of these two transitions, which we identify as [17.8]0(+)-X-1 Sigma(+) and [17.7]1-X-1 Sigma(+); their red-degraded (0,0) band heads lie at 563.0 and 566.2 nm, respectively. The (0,0) band of a new, red-degraded [14.0]1-X-1 Sigma(+) transition at 715.1 nm has also been recorded and analyzed. An accurate set of molecular constants of the three excited states as well as the ground state has been determined by least-squares fitting all of the optical data together with measurements made by other workers of the pure rotational spectrum of AuF in its ground state. These constants include the electronic term energies, vibrational frequencies, rotational constants, and Q-doubling constants. We discuss the nature of these three excited electronic states in terms of the ionic Au+F- electronic configurations from which they are derived.