Agentic Medicine brings a transformative approach to healthcare delivery through multimodal AI agents capable of autonomous clinical reasoning, real-time patient monitoring, and adaptive decision-making. This comprehensive textbook presents the PARM (Planning, Action, Reflection, Memory) framework as a unified architecture for developing AI systems that can independently analyze complex medical data, implement therapeutic interventions, and continuously learn from clinical outcomes across diverse healthcare domains. Agentic Medicine: Multimodal AI Agents in Healthcare systematically examines twenty different clinical applications, from cardiovascular digital twins to respiratory monitoring, emergency department triage to personalized pharmacology, and demonstrates how agentic AI systems integrate multimodal data streams (imaging, genomics, wearable sensors, electronic health records) to provide context-aware clinical support. Each chapter combines theoretical foundations with practical application strategies, addressing critical challenges in bias reduction, explainability, regulatory compliance, and clinical integration. Designed for clinicians, AI researchers, healthcare administrators, and medical informatics professionals, this work bridges the gap between AI capabilities and real-world medical applications, offering visionary perspectives on autonomous healthcare systems and actionable guidance for the development, validation, and deployment of AI agents that improve patient outcomes while maintaining human oversight and ethical standards.