  This is a tutorial on some basic non-asymptotic methods and concepts in
random matrix theory. The reader will learn several tools for the analysis of
the extreme singular values of random matrices with independent rows or
columns. Many of these methods sprung off from the development of geometric
functional analysis since the 1970's. They have applications in several fields,
most notably in theoretical computer science, statistics and signal processing.
A few basic applications are covered in this text, particularly for the problem
of estimating covariance matrices in statistics and for validating
probabilistic constructions of measurement matrices in compressed sensing.
These notes are written particularly for graduate students and beginning
researchers in different areas, including functional analysts, probabilists,
theoretical statisticians, electrical engineers, and theoretical computer
scientists.
