Job advertisements vary in what they request upfront. Minimally, you will be asked to send a letter of application and vita. Some ads also specifically request a dissertation abstract. Whether or not an abstract is explicitly solicited as part of the initial application, you can and should send a dissertation abstract along with your application letter and CV.
Like the letter of application, you should strictly observe the conventions on the length and formatting of the dissertation abstract. The finished document should be two pages, single-spaced, in normal (12 point) font, with standard margins. You should avoid going over two pages (even if it’s just by a line or two). Conversely, it is not to your advantage to shorten it further: when you’re limited to two pages, it doesn’t look good if it appears that you don’t have sufficient material to fill them.
The initial one or two paragraphs of the abstract (approximately half a page) should offer an overview of the project: its issues and methods, other relevant work engaged, stakes and contexts. While you might want to repeat a key sentence or formulation that appears in your letter of application, the opening to the abstract should not simply reproduce the paragraph on the dissertation included in your letter. Think of these opening paragraphs instead as an opportunity to flesh out and supplement what you say in the letter. For example, you might want to foreground a different strand of your argument (something that complements without simply repeating what was headlined in the letter). This opening is also an opportunity to situate your project more fully in relation to relevant scholarship in your field(s). Where the description in your letter most likely had to sound a single note (as in, my dissertation takes up X), here you have the relative luxury of space to detail (the interrelation between) a set of concerns (as in, my dissertation takes up X as it illuminates Y in the context of Z). You might want to conclude these introductory paragraphs by discussing your aspirations for the project– what you aim to achieve; how you hope your intervention will advance this or that scholarly conversation.
The body of the abstract should consist of a detailed chapter outline, in which you explain the main argument (or preoccupation) of individual chapters, specific materials engaged, rationale for that selection, and analytical yield. This is your opportunity to demonstrate the design of the project and, ideally, to show how individual chapters comprise a series of discrete discussions or investigations that cumulatively amount to more than the sum of their parts. This is also your opportunity to foreground your innovation in the choice or juxtaposition of texts, or perhaps original archival research accomplished.
A few cautions: If you choose to enter the job market before finishing and defending the dissertation, you should be sure that individual chapter descriptions are nevertheless complete and persuasive. You should be able to generate a solid and compelling account even of a chapter you may not yet have composed, or finished composing. (If you can’t generate a coherent and detailed description of all your chapters, completed and in progress, it is definitely too early to apply.) Think of the dissertation abstract as an occasion to map out both the broad contours of your dissertation (the overarching concerns; the kind of intervention you seek to make; the readers you aim to hail) and the specific pathways through which you pursue your inquiry. Search committees will notice if portions of the map are missing or vague. Conversely, a finely crafted, readable map will help to persuade them that you can be finished and defended before the start of the next academic year.