The absolute frequency and hyperfine structure of the P ( 98 ) 34 - 0 , R ( 38 ) 32 - 0 , P ( 35 ) 32 - 0 , P ( 112 ) 35 - 0 , R ( 75 ) 33 - 0 , R ( 37 ) 32 - 0 , and P ( 34 ) 32 - 0 transitions of molecular iodine at 531.5 nm are measured using high-resolution spectroscopy based on a narrow-linewidth planar-waveguide external cavity diode laser. The absolute frequencies of the transitions are determined with an uncertainty of 5.7 kHz, while the hyperfine structures are measured with an uncertainty of < 1 k H z . High-precision hyperfine constants are obtained by fitting the measured hyperfine splittings, with an uncertainty of approximately 1 kHz, to a four-term Hamiltonian that includes the electric quadrupole, spin–rotation, tensor spin–spin, and scalar spin–spin interactions. The measured absolute frequencies and hyperfine structures are useful for optical frequency metrology and studies of molecular iodine.