In German, how is this possible?

if you're looking for a general rule, there is none. your books, however, are too strict. real life works different than the etiquette rules someone has set up long ago. if you're always waiting for a formal invitation to use "du" you might wait until kingdom come. :D

as a rule of thumb, "du" is used towards family, friends, relatives, children, people round about your own age, in internet chats and forums, people you meet in casual situations like parties etc.

"Sie" is used towards strangers, older people, authorities, your boss or other people who are higher in hierarchy, bank clerks, shop assistants, doctors etc.

work mates are somewhere in between. in many companies "du" is very common, but not always and everywhere. you should first check what the others do and when you are not sure say "Sie" or ask.

a little advice: if you are on a first name basis with someone that means "du" is appropriate. so if someone introduces himself with his first name to you this is already a broad hint. you don't have to wait for an official permission to use "du".

in situations where you are really unsure, say "Sie". but keep in mind that addressing others with "Sie" is always a sign of distance. may be appropriate in one situation but inappropriate in another. when you overuse it you could come across as too uptight and standoffish.

I may be too informal, but in my experience, I'd never address people my own age with "Sie", always "du". When I worked in Germany, almost all members of staff instantly used "du" with me, which made me feel it was appropriate to do so back. I was never told off, so I don't think this was the wrong thing to do. It sounds like you overuse Sie, whereas I would du almost everyone ;) haha

I find the same. I generally wait until the other person says du to me and hope for the best, or ask. They won't be offended if you ask and it's more polite. You'll probably get incredulous looks as to why you think you;re still per Sie but comes with the territory!

You can use "du" with family, and close friends who are like family. If you are using Sie with family and close friends, that might be overdoing it. Otherwise, you are right that a German will ask you if they want you to use "du."

I have twin citizenship Australian/British. My chum change into entitled to three citizenships. Australia is magnificent with twin citizenship (were when you think about that 2002). don't be attentive to why you're aggravated with the Australians. perchance you're asking the questions interior the incorrect position. you'll prefer to attempt asking the Germans about twin nationality. if you're Australian going to German then you truly truly're likely not likely to get it yet once you're German to Australian then in case you get permission (Beibehaltungsgenehmigun) then you truly truly would good be waiting to maintain your German nationality.