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.
6. On the left, click the more options 
icon of the calendar you wish to share.
7. Share with specific people by clicking Add People.
8. Select recipients from your Contacts to share your calendar with.
9. Click Save.
Note: If you shared your calendar with an individual email address, they'll see your calendar in their "Other calendar" list. If you shared your calendar with an email group, they'll see the calendar in their "Other calendars" list once they click on the link in the email invitation from Webmail Calendar.