These investigations of Gauss strongly influenced both the arithmetical theory of quadratic forms in more than two variables and the subsequent development of algebraic number theory, where quadratic fields are replaced with more general number fields. But the impact was not immediate. Section V of "Disquisitiones" contains truly revolutionary ideas and involves very complicated computations, sometimes left to the reader. Combined, the novelty and complexity made Section V notoriously difficult. Dirichlet published simplifications of the theory that made it accessible to a broader audience. The culmination of this work is his text "Vorlesungen über Zahlentheorie". The third edition of this work includes two supplements by Dedekind. Supplement XI introduces ring theory, and from then on, especially after the 1897 publication of Hilbert's "Zahlbericht", the theory of binary quadratic forms lost its preeminent position in algebraic number theory and became overshadowed by the more general theory of algebraic number fields.