This guide outlines how to programmatically interact with a user's calendar using intents or through the CalendarProvider
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(Needs Attention)
For general usage of intents for interacting with the Calendar which is generally simpler but more limited when compared to content providers, check out this calendar intents guide.
See this tutsplus guide for details on how to add an event to the users calendar using intents.
The Calendar Provider is a repository for a user's calendar events. The Calendar Provider API allows you to perform query, insert, update, and delete operations on calendars, events, attendees, reminders, and so on.
You can check out the official docs for an overview. You can also check out this post for retrieving calendars and this second post for retrieving calendar events.