This book constitutes the proceedings of the First International Joint Conference on Artificial Intelligence for Healthcare, and Hybrid Models for Coupling Deductive and Inductive Reasoning, HC@AIxIA+HYDRA 2025, which took place in Bologna, Italy, during 25-26 October 2025. The 40 full papers included in this book were carefully reviewed and selected from 61 submissions. They were organized in topical sections as follows: Rehabilitation and Human-Robot Interaction; AI for Diagnosis and Medical Imaging; short communications; temporal data modeling and analysis; causal modeling and data reasoning; patient management; neur-symbolic and multi-modal learning; large language models in healthcare; and healthcare applications.