To delete an event, click the event on the calendar, and choose the “Delete” option. If the event is a recurring event, you will also be asked if you want to delete the current event only, future recurrences of the event, or all events in the series (both past and future). Note that if you charge per lesson, deleting an event could affect the student’s billing record and amount they owe.

You can also delete a past event or lesson by going to Calendar -> Lesson History, clicking the event, then clicking "Delete Lesson" in the sidebar.
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Finally, you can delete all events on a single day by clicking the arrow in the corner of the day, then choosing "Delete Events" from the drop down menu that appears.