From the Outlook desktop app:
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On the side panel, select 
People.
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Select New Contact Group from the Ribbon.
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Enter a Name for your new group, then select Add Members to add contacts to your new group.
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When you're finished, select Save & Close.
Edit a contact group.
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On the side panel, select People.
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Go to the contact group you want to update in your list of Contacts and double-click the group to open it.
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From the Ribbon, select Add or Remove Members.
- When you're finished updating, select Save & Close.
Delete a contact group
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On the side panel, select People.
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Go to the contact group that you want to delete from your list of Contacts.
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You can right-click the contact group, select Delete from the menu, or click the group, then select Delete from the Ribbon. Contacts are not deleted, only the contact list.
From the Outlook web app:
Create a contact list
You can create a contact list or add contacts to an existing list.
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On the side panel, select 
People.
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Select the contact you would like to add to a new contact list.
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Select Add to list by either right-clicking the contact or selecting it from the Ribbon, then select New contact list.
Edit a contact list
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On the side panel, select People.
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Select All contact lists, then select Edit by either right-clicking the contact list or selecting it from the Ribbon.
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You'll have the option to rename the contact list, add additional contacts to the list, or add a Description to the list.
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When you are finished, select Save.
Delete a contact list
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On the side panel, select People.
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Select All contact lists, then select Delete by either right-clicking the contact list or selecting it from the Ribbon.
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Select Delete again to confirm. Contacts are not deleted, only the contact list.