This book constitutes the refereed proceedings of the 15th International Conference on the Theory and Application of Diagrams, Diagrams 2026, held in Tallinn, Estonia, during August 25–28, 2026.The 14 full papers, 20 short papers and 9 posters included in this book were carefully reviewed and selected from 57 submissions. They were organized in topical sections as follows: Logical Diagrams; Mathematical Diagrams; Diagrams and Cognition; Diagrams and Computation; and Applications.