This collection of papers - starting with a brilliant review article by one of the masters of the field - gives an excellent view of our present knowledge of matter. Partially basing his work on a variational formulation of quantum mechanics E.H. Lieb links the difficult question of stability of matter with deep problems of functional analysis. In this collection the reader will find general results together with deep insights into quantum systems combined in papers on the structure of atoms and molecules, on the thermodynamics limit, and on stellar structure. The book is suitable as an accompanying text for a graduate course in quantum mechanics.