Many dissertation authors publish their dissertations, in whole or in part. Norms around publishing dissertation material vary from one field to another. For instance, in some scientific fields, it is common to publish individual chapters from the dissertation before it is submitted. In the humanities, it is common to develop a monograph from the dissertation after completing the graduate degree.
Whether you publish before or after submitting your dissertation, it is important to plan ahead when signing publishing contracts or submitting your dissertation. Will the publishing contract you sign permit you to use the article in your dissertation later? How does depositing your dissertation in Deep Blue impact this? Can you use material that you've coauthored in your dissertation or thesis? Check with your advisors about norms in your field. With copyright questions, contact the library copyright office. The U-M Author's Addenda may help you to keep the rights you need when you publish your work.
Thinking about transforming your dissertation into your first book? There are a number of resources out there to help you understand the process of reworking a dissertation for publication as a monograph. It's important to remember that almost no dissertations are ever published as a book without a significant amount of work on the author's part to edit and refocus the manuscript for an audience beyond the dissertation committee.
In reading some of the resources listed above, you might encounter discussions of how having your dissertation available online (for example, in Deep Blue) could negatively impact a publisher's willingness to look at your manuscript. Some authors assert that you should not put your dissertation online if you hope to sign a publishing contract. However, please note there is very little evidence to support this view. In fact, research has shown that publishers will indeed consider manuscripts that are revised versions of openly-accessible dissertations [Ramirez, et al. (2013). Do Open Access Electronic Theses and Dissertations Diminish Publishing Opportunities in the Social Sciences and Humanities? Findings from a 2011 Survey of Academic Publishers. College & Research Libraries, 74(4), 368-380. doi:http://dx.doi.org/10.5860/crl-356].