1. On your computer, open Google Calendar.
   
2. Click an event  Edit event .
   
3. On the right, under "Guests," start typing the name of the person and choose someone from your contacts. You can also type an email address to invite people who aren't in your contacts list.
   
   To mark a guest as optional: Next to the guest's name, click the person's icon . If you don't see the icon, hover over the guest's name.
   
4. When you're done editing your event, click Save.
   

When you save your event, an email invitation will be sent to your guests.

You can't add people to events that are automatically created from Gmail.