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...Lecture notes on non asymptotic theory of random matrices markrudelson amsshortcourseonrandommatrices san diego january partially supported by nsf dms grant introduction the classical matrix is concerned with various spectral characteristics families when dimensions tend to innity there are many examples these character istics which variables themselves converge certain limit laws this includes celebrated wigner semicircle law for empirical measures eigenvalues symmetric marchenko pastur sample covariance tracy widom distribution describing rst singular values a sequence etc limits paramount importance yet in applications one usually needs information about behavior such charac teristics large but xed n instance problems convex geometry constructs section an dimensional body taking kernel or range arise also analysis rates convergence computer science algorithms both cases dimension ambient space remains and seeks explicit estimates probabilities terms knowing little help involving nit...