If the left hand pane with the album is missing and you have problems dragging the source pane to the left as Larry suggested
delete the iPhoto Preference file, com.apple.iPhoto.plist that resided in your Users/Home/Library/Preferences folder. Then launch iPhoto and it should appear.
NOTE: In Lion and Mountain Lion the Home/Library folder is now invisible. To make it permanently visible enter the following in the Terminal application window: chflags nohidden ~/Library and hit the Enter button - 10.7: Un-hide the User Library folder. Then you'll be able to find and delete the preference file.
The 2 replies pointed me in the right direction and I am so grateful for your help!
I was able to see the left hand pane OK, but, to my great surprise, there was a control menu for "albums" there. All I had to do was click it, and all the album names reappeared. In other words, iPhoto allows you to hide or show all your albums, and somehow my album got hidden without my actually knowing that I had done it. Maybe, I had hit the link without knowing.
When my albums reappeared, I shouted in joy, and gave great thanks to the people who took the time to try and help me. Bless you both.