There is no such thing as a “German alphabet”, and while we are at it there is also no such thing as an “English alphabet” either. I don’t really know where this originated, but it appears to be perpetuated by American teachers. To my knowledge, no such concept ever got wide traction anywhere in the German-speaking area. Presumably, for a culture that actually has distinctive features in its writing system, there is less reason to come up with such terminology. (PS: Another explanation would be if such terminology once existed in German but was primarily applied to fraktur letters and cursive handwriting. Not too long ago, many older Germans still considered antiqua and the normal modern handwriting somewhat foreign. I don't know how to test this hypothesis.)
By þe way, in part you have þe Germans to þank for þe simplicity of “þe English alphabet”. Before þe English imported heaps of cheap printing presses from Germany in the 15th or 16th century, þ (thorn) and the rarer ȝ (yogh; used e.g. in McKenȝie but also in þouȝ, ouȝt, bouȝt etc.) were still widely used. Þe shiny new presses didn't come wiþ þese letters (þouȝ þey did have useless umlauts instead), and printers simply substituted th and z/gh/y for þem instead of paying for þe missing types.
There is such a thing as the Latin alphabet. In its modern standard version it consists of 26 letters A–Z. Some of them are of relatively recent, Central European (?) origin:
- The distinction of I and J is new. Originally this was just one letter.
- The distinction of U and V is new. Originally this was just one letter.
- The letter W is new. Originally this was the sequence VV or UU.
One of the original 23 letters was a 'foreign' letter even in Latin: K was originally an Etruscan letter that only appeared in Latin words of Etruscan origin. (The Etruscans were the previous big militaristic culture, which was then taken over by their former vassals, the Romans. Apparently the Etruscans distinguished two different K sounds, only one of which was represented by Latin C.)
Possibly caused (but at least much exacerbated) by the ubiquity of typewriters and later of computers that could only present the very restricted ASCII character set, there is a modern American tradition of totally rejecting not just modified Latin characters but even accented letters that have been fully part of English since practically forever. All major dictionaries are full of English words, mostly of French origin, whose standard spelling has an accent. They do, however, not always agree on the details. Sometimes the accented form is primary in one dictionary and secondary in the other, and for another word the roles are reversed. In many cases such as resume (the noun, not the verb) the accent is critical for fast and efficient communication, even in English. E.g., I only had to add “(the noun, not the verb)” because I used the non-standard, ersatz spelling for resumé which came to be accepted as correct only because sometimes technical difficulties prevent the better spelling. (By the way, resumé is not the French spelling of the word. The French spelling is résumé.)
There is of course such a thing as “the alphabet” as taught to German children. Usually it is presented starting with A–Z, then there is a separate block of the three umlauts ä, ö, and ü, and finally in a third block or at the end of the second, there is ß. This is also the normal order in which children recount the alphabet. Though usually they stop after the first block of 26 letters, or possibly after the second. Except for the lack of nationalist ideology, this is just like American children don’t mention é as part of “the English alphabet”.
Accented and special letters; sorting
Here are two slightly more standard questions:
- The distinction between special letters added to the standard Latin alphabet, and accented versions of (standard or special) letters.
- The sort order when making lists. Fortunately this is less relevant nowadays than it once was.
Generally, an accent is something added at some stage to a letter in an existing spelling in order to distinguish it from other spellings, to indicate that another letter was dropped because it became silent, or for consistency with other spellings that were derived in one of the previous two ways. When it’s technically impossible to print an accent (as used to be the case often for capital letters), it’s acceptable to just drop it. An example is the diaeresis in the English word coöperate (New Yorker spelling).
The two dots in ä, ö, and ü are what remains of the letter e after generations of scribes placed it above the previous vowel in certain situations. When those letters cannot be printed correctly, the only acceptable work-around, ever, is to use ae, oe, or ue instead. Therefore, ä, ö, ü in German are not accented letters, and in particular they are not a, o, u with diaereses. They are special letters designed to be used with the Latin alphabet; they are modified Latin letters. Yet they are not full members of the alphabet.
Similarly, ß evolved out of a ligature for sz at a time when German didn’t really distinguish s and z s and z were used differently than today. The z in this context was later regularised to an s and isn’t optically recognisable anymore (because the z shape has changed), but the letter ß is still often called s z (usually spelled Eszett). When ß is not available, as is always the case when using capitals only since ß has no capital version¹, the only acceptable solution is to replace it by ss. (Definitely not by a single s, and definitely not by β (Greek beta), as is still often done in manuals produced in Asia.) The old alternative work-around of replacing it by sz (which is rare to occur otherwise and can be distinguished from naturally occurring ss) has fallen out of use.
¹ Technically, the lack of a capital version of ß has long been felt to be a problem, and therefore some people came up with uppercase variants of ß. They may be getting a bit more frequent in more modern fonts. However, even if your font has it and you can figure out a key combination to enter it, it's still eccentric to use it and people will notice. (Which is fine if you don't mind taking attention off the content of your text. Though most people will think it looks strange, hardly anyone will get into word rage over this.)
When it comes to sorting names, the standard German point of view is that ä is sorted as ae etc., and ß is sorted as ss. Things become tricky and very chaotic when you have to sort Müller, Mueller, Müllermeister and Muellermeister, for example. There is no established standard for handling this. (Of course there are standards. The problem is that there are too many of them and almost nobody knows when to apply which one.)
The fact that some other languages also make frequent use of letters that look like German umlauts causes additional difficulty. Danish ø is not one of them, but has the same function and much the same history (from oe) as German ö. So does Swedish ö. In Scandinavia, Danish ø and Swedish ö are probably considered fully equivalent variant forms of the same letter; I am just not sure if people distinguish them in names. In sorting, they come after z.
This creates all sorts of problems when you try to sort lots of author names. You must treat ö in a German name as oe and ö in an English or French word as o. You may decide to treat Swedish ö and maybe even Danish ø like German ö, but then whatever you do with Danish å will cause some inconsistency. Not to forget Finnish ä, Hungarian öü, Turkish ü and Chinese pinyin ö, which are all special letters but not umlauts, even though they look and sound exactly like the German umlauts². Using the rules of the original language is no help if someone was born in one country and ended up in the other, possibly turning German ö in a German name of Danish origin into a Swedish ö.
² An umlaut is a specific type of modification of a base vowel for grammatical reasons which occurs in Germanic languages. Remnants in English: brother -> brethren, fall → fell, foot → feet, old → elder, long → length, full → fill. Nobody adopts umlauts, of course, but the graphical appearance of the German umlauts seems to be a big cultural export hit.
Recognizing that there will be some variation between Germany, Austria, Switzerland, etc.
I am not aware of any variation between the German-speaking countries. There seems to be no reason for one anyway. Of course, ß is not used in Switzerland, but that just means that the most rarely mentioned part of the alphabet is never mentioned there. By the way, the practice of not using ß in Switzerland seems to have started only with typewriters. The reason is that Swiss typewriters had (and computer keyboards have) the same number of keys as English and German keyboards but need to accommodate more letters so that all four national languages can be typed easily. So they decided to leave out ß and the capital umlauts, starting a process of kicking them out altogether.
Update: Capital ß
After capital versions of ß became increasingly available in fonts, and since they are important for correct all-capital spelling of names in passports, the international Council for German Orthography decided in 2017 that they now exist officially. However, capital ß is still just as hard to type on a German keyboard as any other exotic letter, and in particular harder than é. And it still looks pretty crappy in all fonts. So it seems best to continue avoiding it unless you really need it for technical reasons.