Our understanding of how the gut microbiome interacts with its human host has been restrained by limited access to longitudinal datasets to examine stability and dynamics, and by having only a few isolates to test mechanistic hypotheses. Here, we present the Broad Institute-OpenBiome Microbiome Library (BIO-ML), a comprehensive collection of 7,758 gut bacterial isolates paired with 3,632 genome sequences and longitudinal multi-omics data. We show that microbial species maintain stable population sizes within and across humans and that commonly used 'omics' survey methods are more reliable when using averages over multiple days of sampling. Variation of gut metabolites within people over time is associated with amino acid levels, and differences across people are associated with differences in bile acids. Finally, we show that genomic diversification can be used to infer eco-evolutionary dynamics and in vivo selection pressures for strains within individuals. The BIO-ML is a unique resource designed to enable hypothesis-driven microbiome research.