This book constitutes the refereed proceedings of the Third International Joint Conference on Conceptual Knowledge Structures, CONCEPTS 2026, held in Montpellier, France, during August 31– September 4, 2026.The 18 full papers and 7 short papers included in this book were carefully reviewed and selected from 42 submissions. They were organized in following topical sections: Closing an Open Problem; Theory; Algorithms; Data Analysis; and Applications. Additionally, there are 11 Nectar papers included in this volume highlighting recent contributions from members of the conceptual structures community that have appeared in other venues.