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Abstract The CO(1–0) line has been carefully calibrated as a tracer of molecular gas mass. However, recent studies often favor higherJtransitions of the CO molecule, which are brighter and accessible for redshift ranges where CO(1–0) is not. These lines are not perfect analogs for CO(1–0), owing to their more stringent excitation conditions, and must be calibrated for use as molecular gas tracers. Here, we introduce the Arizona Molecular ISM Survey with the SMT, a multi-CO line survey ofz∼ 0 galaxies conducted to calibrate the CO(2–1) and CO(3–2) lines. The final survey includes CO(2–1) spectra of 176 galaxies and CO(3–2) spectra for a subset of 45. We supplement these with archival CO(1–0) spectra from xCOLD GASS for all sources and additional CO(1–0) observations with the Kitt Peak 12 m Telescope. Targets were selected to be representative of the 10⁹M_⊙≤M_*≤ 10^11.5M_⊙galaxy population. Our project emphasized careful characterization of statistical and systematic uncertainties to enable studies of trends in CO line ratios. We show that optical and CO disk sizes are on average equal, for both the CO(1–0) and CO(2–1) line. We measure the distribution of CO line luminosity ratios, finding medians (16th–84th percentile) of 0.71 (0.51–0.96) for the CO(2–1)-to-CO(1–0) ratio, 0.39 (0.24–0.53) for the CO(3–2)-to-CO(1–0) ratio, and 0.53 (0.41–0.74) for the CO(3–2)-to-CO(2–1) ratio. A companion paper presents our study of CO(2–1)'s applicability as a molecular gas mass tracer and search for trends in the CO(2–1)-to-CO(1–0) ratio. Our catalog of CO line luminosities is publicly available.