
Flexible, RESTful access to the user's inbox.
Gmail API is a free Business API that requires OAuth authentication, is served over HTTPS and has unconfirmed CORS support.
Details from developers.google.com.

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The Gmail API is provided by Google for Developers (developers.google.com).
Yes. The Gmail API is listed in the Business category of the public-apis directory, which only includes APIs that are free or have a free tier. Check its documentation for rate limits and paid plans.
Yes. The Gmail API uses OAuth authentication, so you need to register for credentials before making requests.
CORS support for the Gmail API is unknown. Test a request from the browser, and fall back to a server-side call if it is blocked.
Yes. The Gmail API is served over HTTPS, so it's safe to use in production.