This book constitutes the proceedings of the First International Joint Conference on Conceptual Knowledge Structures, CONCEPTS 2024, which took place in Cádiz, Spain, during September 9-13, 2024. The conference is an amalgamation of the 18th International Conference on Formal Concept Analysis (ICFCA); the 17th International Conference on Concept Lattices and Their Applications (CLA); and the 28th International Conference on Conceptual Structures (ICCS). The 18 full and 4 short papers included in this book were carefully reviewed and selected from 38 submissions. They were organized in topical sections as follows: Theory; algorithms, methods, and resources; applications. .