The Poincare Seminar is held twice a year at the Institute Henri Poincare in Paris. The goal of this seminar is to provide up-to-date information about general topics of great interest in physics. Both the theoretical and experimental results are covered, with some historical background. Particular care is devoted to the pedagogical nature of the presentation.This volume contains the lectures of the third and fourth Poincare Seminar, both held in 2003. The third one is devoted to Bose-Einstein Condensation: it covers the physics of superfluid liquid helium as well as the recently discovered atomic Bose-Einstein condensates. Major experimental results are presented, together with relevant theoretical approaches and remaining open questions. The fourth one concentrates on Entropy, giving a comprehensive account of the history and various realizations of this concept, from thermodynamics to black holes, and including theoretical and experimental discussions of the corresponding fluctuations for mesoscopic systems near equilibrium.Contributing authors:Roger BalianSebasten BalibarClaude Cohen-TannoudjiJean DalibardThibault DamourOlivier DarrigolChristian MaesPhilippe NozieresFelix RitortChristophe SalomonGora V. Shlyapnikov