It was my understanding that 'ß' is a double 's' and can be written with as 'ss', especially for computer applications which don't offer the 'ß' character. However, why are some words with 'ss' not written with a 'ß'? (z.B. müssen, not müßen?) And is it incorrect for me to write müßen? To be honest, I ask because I like using the 'ß' character due to the novelty.
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Well, no. ß is a ligature (s + z, in case you were wondering) and must be used for certain words (with the exception of Switzerland, who abolished it quite some time ago and simply use ss everywhere instead.) If your keyboard does not have it (or you are writing IN ALL CAPS) you may use ss (SS) instead, but that's really an exception.
Before the orthography reform of 1996 the use of ß was much more widespread. These days, it's only used following a long vowel, as a rule. It's probably best to pick up the correct spelling when learning a new word. In that sense it might be easier than for native speakers who went to school ages ago, like yours truly :)
Yes, it's müssen.
According to Zwiebelfisch, there are four rules:
There is an interesting exception (that very few people are aware of): In case of a possible misunderstanding, SZ is used to replace ß when writing in capitals: "ER TRANK IN MASZEN"
As an American Student who is constantly struggling with my German grammer, I would like to point out that the use ss in place of ß (Eszett [das]) in many words (e.g. müssen) is only since the latest Rechtschreibreform mentioned above. In fact, just before the official publication of the Rechtschreibreform, there was a website titled (translated): "Save the Eszett".