They all cover elementary number theory, Dirichlet's theorem, quadratic fields and forms, and sometimes more advanced topics.
Dedekind added several appendices to the Vorlesungen, in which he collected further results of Lejeune Dirichlet's and also developed his own original mathematical ideas.
These chapters can be thought of as a summary of existing knowledge, although Dirichlet simplifies Gauss's presentation, and introduces his own proofs in some places.
Supplement VI contains Dirichlet's proof that an arithmetic progression of the form a+nd where a and d are coprime contains an infinite number of primes.
Aus der elementare Zahlentheorie in 1950, with an English translation in 1958 under the title Elementary number theory.
Volume 1 on elementary and additive number theory includes the topics such as Dirichlet's theorem, Brun's sieve, binary quadratic forms, Goldbach's conjecture, Waring's problem, and the Hardy–Littlewood work on the singular series.