This book constitutes the proceedings of the First International Workshop on Topology- and Graph-Informed Imaging Informatics, TGI3 2024, held in conjunction with the 27th International conference on Medical Image Computing and Computer Assisted Intervention, MICCAI 2024, in Marrakesh, Morocco in October 2024.The 13 full papers presented here were carefully reviewed and selected. These papers focus on the application of Topological Data Analysis (TDA) techniques, along with other computational techniques, for summarizing, analyzing, quantifying, and visualizing complex medical data for a more effective and efficient analysis.