This book constitutes the First Segmentation of the Aorta Challenge, SEG.A. 2023, which was held in conjunction with the 26th International Conference on Medical Image Computing and Computer-Assisted Intervention, MICCAI 2023, on October 8, 2023. The 8 full and 3 short papers presented have been carefully reviewed and selected for inclusion in the book. They focus specifically on robustness, visual quality and meshing of automatically generated segmentations of aortic vessel trees from CT imaging. The challenge was organized as a "container submission" challenge, where participants had to upload their algorithms to Grand Challenge in the form of Docker containers. Three tasks were created for SEG.A. 2023.