This is an announcement for the paper "Non-asymptotic theory of random matrices: extreme singular values" by Mark Rudelson and Roman Vershynin. Abstract: The classical random matrix theory is mostly focused on asymptotic spectral properties of random matrices as their dimensions grow to infinity. At the same time many recent applications from convex geometry to functional analysis to information theory operate with random matrices in fixed dimensions. This survey addresses the non-asymptotic theory of extreme singular values of random matrices with independent entries. We focus on recently developed geometric methods for estimating the hard edge of random matrices (the smallest singular value). Archive classification: math.FA Mathematics Subject Classification: 46B09; 60B20 Remarks: Submission for International Congress of Mathematicians, Hydebabad, India, 2010 Submitted from: romanv@umich.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1003.2990 or http://arXiv.org/abs/1003.2990