We derive cosmological constraints on the matter density, om, and the amplitude of fluctuations, sig, using $mathtt{GalWCat19}$, a catalog of 1800 galaxy clusters we identified in the Sloan Digital Sky Survey-DR13 spectroscopic data set using our GalWeight technique to determine cluster membership citep{Abdullah18,Abdullah19}. By analyzing a subsample of 756 clusters in a redshift range of $0.045leq z leq 0.125$ and virial masses of $Mgeq 0.8times10^{14}$ hm ~with mean redshift of $z = 0.085$, we obtain om ~$=0.310^{+0.023}_{-0.027} pm 0.041$ (systematic) and sig ~$=0.810^{+0.031}_{-0.036}pm 0.035$ (systematic), with a cluster normalization relation of $sigma_8= 0.43 Omega_m^{-0.55}$. There are several unique aspects to our approach: we use the largest spectroscopic data set currently available, and we assign membership using the GalWeight technique which we have shown to be very effective at simultaneously maximizing the number of {it{bona fide}} cluster members while minimizing the number of contaminating interlopers. Moreover, rather than employing scaling relations, we calculate cluster masses individually using the virial mass estimator. Since $mathtt{GalWCat19}$ is a low-redshift cluster catalog we do not need to make any assumptions about evolution either in cosmological parameters or in the properties of the clusters themselves. Our constraints on om ~and sig ~are consistent and very competitive with those obtained from non-cluster abundance cosmological probes such as Cosmic Microwave Background (CMB), Baryonic Acoustic Oscillation (BAO), and supernovae (SNe). The joint analysis of our cluster data with Planck18+BAO+Pantheon gives om ~$=0.315^{+0.013}_{-0.011}$ and sig ~$=0.810^{+0.011}_{-0.010}$.
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