This book constitutes the proceedings of the 24th International Conference on Conceptual Structures, ICCS 2019, held in Marburg, Germany, in July 2019. The 14 full papers and 6 short papers presented were carefully reviewed and selected from 29 submissions. The proceedings also include one of the two invited talks. The papers focus on the representation of and reasoning with conceptual structures in a variety of contexts. ICCS 2019's theme was entitled "Graphs in Human and Machine Cognition."