In Outlook.com, under "People", there used to be a listing called "Groups" allowing management of same. Today, Groups listing is gone! How can I manage my contact groups?
It appears that groups are now just listed in the alphabetical listing on the left side, in amongst all of your contacts. Simply scroll down to find your group, click it, then you'll be able to edit it.
As you can see from my screen shot, my two groups, "test" and "Test2" have an icon to indicate that they're groups. Clicking it adds "Edit" and "Delete" to the menu bar at the top of the screen.
Note: you have to click on the group name, NOT check the box next to it, to get the "edit" and "delete" menu. Checking the box, you get "Manage" option which gives "Add People" option but you can't add from your Hotmail/Outlook contact list!
Why they decided to make this change, I don't know. (There doesn't appear to be any sort of blog or change log.) It seems a little counter-intuitive to me. It does, however, keep the interface very clean, which I believe is one of the ways they're trying to differentiate themselves from Gmail.
There's an even better way to do this in Outlook.com. In the Outlook People category scroll to the bottom off your contacts and look for the red box with a white # character in it. Click on this red box and you will get this index, instead of only 2 groups, now you've got 26 groups, all created automatically: