Three basic principles -- The large sieve -- Arithmetic formulations of the large sieve -- A weighted sieve and its application -- A lower bound of Roth -- Classical mean value theorems -- New mean value theorems -- Large moduli theorems -- Further results and conjectures concerning mean and large moduli -- Mean moduli of L-functions -- Zero-free regions and the proliferation of zeros -- Distribution of zeros of L-functions -- Least character non-residues and arg L(12+it, x) -- The prime number theorems of Hoheisel and Selberg -- The bombieri — Vinogradov theorem -- A lemma in additive prime number theory -- The mean value theorem of Barban.