I examine Richard Dedekind's important contributions to set theory. These contributions are made in his mathematical work and I present an exposition of several of his mathematical papers. I develop my paper in the following sections:

1. Dedekind's first contacts with the concept of set [1855-1858]

2. The manuscript of 1858 and the paper of 1872

3. «Supplement X» of Dirichlet's Lectures on Number Theory, second edition [1871]

4. The text of 1888 and the manuscript of 1872-1878

5. An unpublished manuscript of 1887-1897: the dangers of set theory

6. The unpulished manuscripts of 1887 and 1889

7. Dedekind and topology

8. Conclusion

and I show that Dedekind's contributions to set theory are very important and that without them possibly the introduction of set theory into mathematicical work might have appeared later that it did.