Let \(x\) be a complex random variable with mean zero and bounded variance \(\sigma^2\). Let \(N_n\) be an \(n\times n\) random matrix with entries being i.i.d. copies of \(x\) and let \(\lambda_1,\dots,\lambda_n\) be eigenvalues of \(\frac1{\sigma\sqrt n}N_n\). The paper under review is a contribution to the research related to the circular law conjecture: \(\mu_n(s,t)=\frac1n\#\{k\leq n\mid \text{Re}(\lambda_k)\leq s; \text{Im}(\lambda_k)\leq t\}\) tends to the uniform distribution \(\mu_{\infty}\) over the unit disk as \(n\to\infty\). The authors prove (under a slightly stronger assumption) this conjecture with strong convergence. The proof is based on a new general result about the least singular value of random matrices.