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When you code HTML emails (as in those fancy newsletters that you get in your email inbox), you do not code them the same way that you would code for a web page. This is because HTML emails are rendered by email clients such as Microsoft Outlook and Thunderbird, rather than by your browsers.
Even if users are viewing the HTML emails in webmail such as Yahoo, Hotmail, or Gmail, your HTML are still run through the webmail client engine.
To ensure that your HTML email renders okay on most email and webmail clients, there are a few guidelines that you should adhere to.
In general, ...
Tizag.com shows what is meant by inline CSS with the style attribute.
Don't use "advanced" or "obsure" CSS rules. CampaignMonitor.com has a table of what CSS properties are accepted by the various email clients. And so does XavierFrenette.com.
Here are some articles on building HTML emails:
Sitepoint's How to Code HTML Email Newsletter
MailChimp has some more tips listed.
One of the more difficult email client to get newsletters to look good in is Microsoft Outlook 2007 because it uses the Microsoft Word rendering engine. Here are more details and what markup the email client supports, or in this case not support.
And, by the way, if you are sending out HTML Newsletters, you should be aware of the requirements of the CANSPAM Act which requires that the content not be misleading, that there is an unsubscribe link, and that there is a physical postal address in your newsletters.
ReturnPath has some tools that help you see what your HTML newsletter looks like in various mail clients.