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On your Calendar, Select the Event you want to Invite people to. Or create an event. On your mobile device, scroll down and touch Invite people. On a computer, find the Add guests section on the right. Start typing the name of the person and choose a result from your contacts. You can also type an email address to invite people who aren't in your contacts list. When you're done editing your event, select Save. When you save your event, an email invitation will be sent to your guests.

https://support.google.com/calendar/answer/37161?hl=en