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Starting with Thunderbird 38, the calendaring extension Lightning has been packaged with Thunderbird. This is a big advantage for previous Lightning users, because a compatible version of Lightning is always available with Thunderbird. It is also a great opportunity for Thunderbird users that haven't been using Lightning as it becomes easier to process emails that contain invitations.
Maintain your schedule locally using the pre-created "Home" calendar, or synchronize with a remote calendar using iCalendar files on a WebDAV server or a calendaring server supporting the CalDAV protocol. There are also extensions available for enhanced Google Calendar support and Microsoft Exchange among others. You can find them on addons.mozilla.org. An article on creating new calendars is available for more information.
For more information, read the article on using Lightning or visit the calendar overview page for support topics.
This integration of course does not mean that you must use Lightning. If you haven't used Lightning before, you can do this directly from the notification bar at the bottom of the Thunderbird window.
You are also free to disable Lightning at any time in the addons manager, but in order to make it easier to identify future issues, it is recommended that you leave it enabled and hide the features you do not use. There should not be a significant performance impact, especially when you have not added any events. You can hide the "Today Pane" by clicking the button in the status bar at the bottom of the screen.