What is Alec’s Condolence Book?

Alec’s condolence book is a symbol of a source of personal information. Gustav uses this condolence book to learn Peter’s real name and his home address. Even though he is a secret service agent, Peter did not think to use a fake name in the book or not include his address. It is very likely this entry in Alec’s condolence book is why Peter was called in for questioning while Smiley, who was more difficult to locate, was not.