The Poincaré Seminar is held twice a year at the Institut Henri Poincaré in Paris. This volume contains the lectures of the 2002 seminars. The main topic of the first one was the vacuum energy, in particular the Casimir effect and the nature of the cosmological constant. The second one concentrated on renormalization, giving a comprehensive account of its mathematical structure and applications to high energy physics, statistical mechanics and classical mechanics.Students will find excellent introductions to the subjects with further lectures leading to the frontiers of experimental and theoretical research, scientists will profit from contributions by outstanding experts.