Dirichlet (1805–1859) is well known for his significant contributions to several branches of mathematics. In number theory, for instance, he proved the conjecture by Gauss that there are infinitely many primes in any arithmetic progression such that the first term and the relative difference are relatively prime. He introduced Dirichlet series to analytic number theory, a tool which continues to be important today. In analysis, he is remembered for his work in potential theory, especially his study of harmonic functions with prescribed boundary values, now known as the Dirichlet problem. He is also known for his work on trigonometric series, in particular his rigorous proofs of conditions for their convergence which settled Cauchy's objections to Fourier's earlier work. He also made contributions to the theory of ideals.

The two volumes of Dirichlet's Collected Works are published here in a single volume. Certain handwritten manuscripts from Dirichlet's Nachlass have been included by the editors: Kronecker and Fuchs. They have also included some of the mathematical correspondence that Dirichlet had with Gauss and Kronecker.