The gene-regulatory landscape of the brain is highly dynamic in health and disease, coordinating a menagerie of biological processes across distinct cell types. Here, we present a multi-omic single-nucleus study of 191,890 nuclei in late-stage Alzheimer’s disease (AD), accessible through our web portal, profiling chromatin accessibility and gene expression in the same biological samples and uncovering vast cellular heterogeneity. We identified cell-type-specific, disease-associated candidate cis-regulatory elements and their candidate target genes, including an oligodendrocyte-associated regulatory module containing links to APOE and CLU. We describe cis-regulatory relationships in specific cell types at a subset of AD risk loci defined by genome-wide association studies, demonstrating the utility of this multi-omic single-nucleus approach. Trajectory analysis of glial populations identified disease-relevant transcription factors, such as SREBF1, and their regulatory targets. Finally, we introduce single-nucleus consensus weighted gene coexpression analysis, a coexpression network analysis strategy robust to sparse single-cell data, and perform a systems-level analysis of the AD transcriptome.