You can create a new calendar and invite other people to view or edit it. When you create an event, you'll see an option to choose which calendar to add the event to.
1. Click the Mail Drop-down menu in the top left corner, select Calendar from the menu. The Calendar will open to the monthly view by default. The are several view types.
2. On the left, above "My Calendars," click Add Calendar
3. Add a calendar name.
4. Select the appropriate Time Zone for you.
5. Click Create calendar.