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This collection of papers - starting with a brilliant article by one of the masters of the field - gives an excellent current review of our knowledge of matter. Partially basing his own work on a variational formulation of quantum mechanics, E.H. Lieb links the difficult question of the stability of matter with important problems in functional analysis. Here the reader will find general results together with deep insights into quantum systems combined with papers on the structure of atoms and molecules, the thermodynamic limit, and stellar structures. The book is suitable as an accompanying text or recommended reading for a graduate course in quantum mechanics. In the third edition, two new sections were added: one contains papers on quantum electrodynamics, and the other on Boson systems. In this fourth edition, these topics have been further developed, extending the book by approximately 120 pages.