As part of a comprehensive review on molecular oxygen spectroscopy, we have measured rotational spectra of isotopic forms of molecular oxygen in its a(1)Δ(g) electronic state with high-resolution terahertz spectroscopy. The data are recorded in close proximity to predicted positions. Due to the high resolution and good signal-to-noise ratio, the fundamental hyperfine parameters eQq and C(I) are determinable for (17)O-substituted species for the first time. A refined nuclear spin orbit coupling constant, a = -211.9328(283) MHz, was determined, and is roughly two orders of magnitude more precise than values determined from near infrared spectroscopy or electron spin resonance studies. Vibrationally excited oxygen in the a(1)Δ(g) electronic state was also observable with small signal levels for many of the rotational transitions.