A survey on current results in Theory of Lieb-Thirring inequalities

About two months ago, jointly with R.Frank and T.Weidl, I published the book "Schrödinger Operators: Eigenvalues and Lieb-Thirring Inequalities" printed by Cambridge University Press. We shall discuss some results from this book that reflect the modern state of art from this area of Analysis and Mathematical Physics. The book appeared in the series Cambridge Studies in Advanced Mathematics.