This is an announcement for the paper "Invertibility of random matrices: norm of the inverse" by Mark Rudelson. Abstract: Let A be an n by n matrix, whose entries are independent copies of a centered random variable satisfying the subgaussian tail estimate. We prove that the operator norm of A^{-1} does not exceed Cn^{3/2} with probability close to 1. Archive classification: Functional Analysis Mathematics Subject Classification: 15A52, 46B09 Remarks: 25 pages The source file(s), square-matrix.tex: 58844 bytes, is(are) stored in gzipped form as 0507024.gz with size 18kb. The corresponding postcript file has gzipped size 94kb. Submitted from: rudelson@math.missouri.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0507024 or http://arXiv.org/abs/math.FA/0507024 or by email in unzipped form by transmitting an empty message with subject line uget 0507024 or in gzipped form by using subject line get 0507024 to: math@arXiv.org.