This book constitutes the proceedings of the First MICCAI Challenge Multi-class Segmentation of the Aorta, AortaSeg 2024, held in conjunction with MICCAI 2024, as a virtual event, during October 2024. The 10 papers included in the book were carefully reviewed and selected from 16 submitting teams. This challenge aimed to advance the field of medical image segmentation by introducing the first large-scale, publicly available dataset for multi-class segmentation of the aorta, its branches, and clinically relevant zones in computed tomography angiography (CTA).