The authors investigate the Cauchy problem for a scalar conservation law \[ u_t+\text{div}_x\varphi(u)=f \quad \text{on } Q=(0,T)\times{\mathbb R}^n; \tag{1} \]
\[ u(0,x)=u_0(x)\in L^1({\mathbb R}^n). \tag{2} \] The flux vector \(\varphi(u)=(\varphi_1(u),\ldots,\varphi_n(u))\) is assumed to be locally Lipschitz continuous, \(f\in L^1(Q)\). It is known that there is the unique mild solution of the problem under consideration which can be constructed on the base of nonlinear semigroup theory. This solution coincides the generalized entropy solution (in Kruzhkov’s sense) if the function \(u_0\) and \(f\) are bounded but in the general \(L^1\)-setting the function \(\varphi(u)\) may fail to be locally integrable and the equation (1) isn’t correctly defined in the sense of distributions. The authors use an idea of renormalization to generalize the notion of entropy solution. They define a renormalized entropy solution to the problem (1), (2) and prove its existence and uniqueness. It is also shown that the renormalized solution is always the unique mild solution of the problem (1), (2).