Try deleting the com.apple.AddressBook.plist. Quit Address Book. Go to your user folder and select Library/Preferences/com.apple.AddressBook.plist. Move it to your desktop.
Open the application and test. If it works okay, delete the plist from the desktop.
If the application is the same, return the .plist to where you got it from, overwriting the newer ones.
You are welcome. I normally see people recommending 10 - 15% of the hard drive be empty. Since it is only one application, I doubt the empty hard drive space would be the problem.
Try setting up another admin user account to see if the same problem continues. If Back-to-My Mac is selected in System Preferences, the Guest account will not work. The intent is to see if it is specific to one account or a system wide problem. This account can be deleted later.
If the problem is still there, try booting into the Safe Mode using your normal account. Disconnect all peripherals except those needed for the test. Shut down the computer and then power it back up. Immediately after hearing the startup chime, hold down the shift key and continue to hold it until the gray Apple icon and a progress bar appear. The boot up is significantly slower than normal. This will reset some caches, forces a directory check, and disables all startup and login items, among other things. When you reboot normally, the initial reboot may be slower than normal. If the system operates normally, there may be 3rd party applications which are causing a problem. Try deleting/disabling the third party applications after a restart by using the application un-installer. For each disable/delete, you will need to restart if you don't do them all at once.
Thanks again, Eric. I went through the steps, no problem in Address book when using it from another account, other steps made no difference. But problem solved as follows: I remembered that I had created a smart group with four rules, and problems started after that, I realised. I tried to delete the smart group, Address Book froze, I did force quit, and on reopening the smart group had disappeared and with it the problem! When I recreated the smart group, using the same rules (include any card which is a member of any of four groups - none of them a smart group) - the problem returned, and when trying to delete the smart group the same freeze recurred. On reopening Address Book the smart group had again been deleted, and the problem had again disappeared.
Your advice suggested the question: what is the crucial difference between Address book in my account and in another account on my computer, and then I remembered new rule I had created.