Adobe's PDF format is used so consistently as an e-book format that it would be foolish not to mention it. Many programs (such as Word and OpenOffice.org) export directly to PDF, and the files can be opened and read in many applications. In fact, before dedicated e-reader devices made significant inroads into the market, most e-books were just PDF distillations of their print counterparts.
However, it's generally not a good idea to try to use PDF as a source format. Because it's designed to precisely reproduce printed pages, a PDF document needs to be taken apart and put back together if it's being used as a source format for a non-PDF e-book. As a result, PDF should only be used as a source for other e-book formats if you have no choice.
Odds are you won't have just one destination format for your e-book, but several. If your target readers are using a variety of devices -- a Nook, a Kindle, an iPad -- it helps to support as many of those devices as possible. The Kindle, for instance, is notorious for not supporting ePub format files.
These are the most common e-book destination formats and their quirks.
An open, non-proprietary format that uses XHTML as the basis for its document format, ePub is widely supported as an output format by various e-book production applications -- iTunes, for instance, only accepts ePub as a source format. In fact, it couldn't hurt to render a copy of your product as ePub no matter what other formats you're also planning to output to.
EPub has a few downsides. Its formatting methodology assumes that the text will be reflowed to fit the target device, so books that require PDF-style page fidelity won't work well in ePub. Also, there's no support for equations, apart from inserting them as images -- TeX or MathML, two commonly used languages for representing math, aren't supported. And ePub doesn't have a standard way to interpret or share annotations, which might be another drawback for people publishing digital textbooks.
To that end, it's best for "straight" text, or for documents where reflowed formatting won't be an issue.
Mobi and Kindle
A variant of an earlier version of ePub, Mobi -- or Mobipocket -- was developed by the company of the same name as a format to be used with its e-book reader software, designed originally for PDAs and later smartphones. After Amazon bought the company, it made Mobi into the basis for the Kindle reader's own e-book format. Mobi supports digital rights management, but unencrypted Mobi documents can be read on the Kindle without issues.
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