A-genome diploid wheats represent the earliest domesticated and cultivated wheat species in the Fertile Crescent and include the donor of the wheat A sub-genome. The A-genome species encompass the cultivated einkorn (Triticum monococcum L. subsp. monococcum), wild einkorn (T. monococcum L. subsp. aegilopoides (Link) Thell.), and Triticum urartu. We evaluated the collection of 930 accessions in the Wheat Genetics Resource Center (WGRC) using genotyping by sequencing and identified 13,860 curated single-nucleotide polymorphisms. Genomic analysis detected misclassified and genetically identical (>99%) accessions, with most of the identical accessions originating from the same or nearby locations. About 56% (n = 520) of the WGRC A-genome species collections were genetically identical, supporting the need for genomic characterization for effective curation and maintenance of these collections. Population structure analysis confirmed the morphology-based classifications of the accessions and reflected the species geographic distributions. We also showed that T. urartu is the closest A-genome diploid to the A-subgenome in common wheat (Triticum aestivum L.) through phylogenetic analysis. Population analysis within the wild einkorn group showed three genetically distinct clusters, which corresponded with wild einkorn races α, β, and γ described previously. The T. monococcum genome-wide F_ST scan identified candidate genomic regions harboring a domestication selection signature at the Non-brittle rachis 1 (Btr1) locus on the short arm of chromosome 3Am at ∼70 Mb. We established an A-genome core set (79 accessions) based on allelic diversity, geographical distribution, and available phenotypic data. The individual species core set maintained at least 79% of allelic variants in the A-genome collection and constituted a valuable genetic resource to improve wheat and domesticated einkorn in breeding programs.