The first optical investigation of the spectra of diatomic PdC has revealed that the ground state has Omega=0(+), with a bond length of r(0)=1.712 A. The Hund's case (a) nature of this state could not be unambiguously determined from the experimental data, but dispersed fluorescence studies to be reported in a separate publication, in combination with a comparison to theoretical calculations, demonstrate that it is the 2 delta(4) 12 sigma(2), (1)Sigma(0+)(+) state, which undergoes spin-orbit mixing with a low-lying 2 delta(4) 12 sigma(1) 6 pi(1), (3)Pi(0)(+) state. An excited (3)Sigma(+) state with r(e)=1.754 +/- 0.003 A (r(0)=1.758 +/- 0.002 A) and Delta G(1/2)=794 cm(-1) is found at T-0=17 867 cm(-1). Although only the Omega=1 component of this state is directly observed, the large hyperfine splitting of this state for the Pd-105 C-12 isotopomer implies that an unpaired electron occupies an orbital that is primarily of 5s character on Pd. Comparison to ab initio calculations identifies this state as 2 delta(4) 12 sigma(1) 13 sigma(1), (3)Sigma(1)(+). To higher wavenumbers a number of transitions to states with Omega=0(+) have been observed and rotationally analyzed. Two groups of these have been organized into band systems, despite the clear presence of homogeneous perturbations between states with Omega=0(+) in the region between 22 000 and 26 000 cm(-1).