The two-volume set LNCS 15679 and 15680 constitutes the refereed proceedings of the 14th International Conference on Algorithms and Complexity, CIAC 2025, held in Rome, Italy, during June 10-12, 2025. The 44 full papers included in these proceedings were carefully reviewed and selected from 110 submissions. They focus on all aspects of important venue for researchers working on computational complexity and the design, analysis, experimentation, and application of efficient algorithms and data structures.