  Consider the empirical spectral distribution of complex random $n\times n$
matrix whose entries are independent and identically distributed random
variables with mean zero and variance $1/n$. In this paper, via applying
potential theory in the complex plane and analyzing extreme singular values, we
prove that this distribution converges, with probability one, to the uniform
distribution over the unit disk in the complex plane, i.e. the well known
circular law, under the finite fourth moment assumption on matrix elements.
