accent acute accent ( ´ ) double acute accent ( ˝ ) grave accent ( ` ) double grave accent (  ̏ ) breve ( ˘ ) caron / háček ( ˇ ) cedilla ( ¸ ) circumflex ( ^ ) diaeresis / umlaut ( ¨ ) dot ( · ) anunaasika ( ˙ ) anusvara (  ̣ ) chandrabindu (   ँ   ঁ   ઁ   ଁ ఁ ) hook / dấu hỏi (  ̉ ) horn / dấu móc (  ̛ ) macron ( ¯ ) ogonek ( ˛ ) ring / kroužek ( ˚, ˳ ) rough breathing / spiritus asper (  ῾ ) smooth breathing / spiritus lenis (  ᾿ ) apostrophe ( ' ) bar ( | ) colon ( : ) comma ( , ) hyphen ( ˗ ) tilde ( ~ ) titlo (  ҃ ) The umlaut mark (or simply umlaut) and the diaeresis mark (or simply diaeresis) or trema are two diacritics consisting of a pair of dots placed over a letter. When the vowel is an i, the diacritic replaces the tittle. The two diacritics are very similar in appearance, and the distinction between them is not always made.
The diaeresis or trema is the diacritic mark ( ¨ ), used to indicate a phonological diaeresis, or, more generally, that a vowel should be pronounced apart from the letter which precedes it. For example, in the spelling coöperate, it reminds the reader that the word has four syllables [koʊˡɔpəreɪt], not three [ˈkuːpəreɪt]. In English, the trema is rare, and not mandatory, but other languages like Dutch, Spanish, and French make regular use of it. By extension, the words trema and diaeresis also designate the same diacritic when used to denote other kinds of sound changes, such as marking the schwa ë in Albanian.
The umlaut is a similar-looking diacritic ( ¨ ) which indicates a phonological umlaut in German. The umlauted vowels are ä, ö, and ü. The same name is used in other languages which have borrowed these symbols from German.
In professional typography, umlaut dots are usually a bit closer to the letter's body than the dots of the trema.

Diaeresis or trema
Punctuation
apostrophe ( ' ' ) brackets ( ), [ ], { }, < > colon ( : ) comma ( , ) dashes ( ‒, –, —, ― ) ellipsis ( …, ... ) exclamation mark ( ! ) full stop/period ( . ) guillemets ( « » ) hyphen ( -, ‐ ) question mark ( ? ) quotation marks ( ' ', " " ) semicolon ( ; ) slash/stroke ( / ) solidus ( ∕ ) spaces ( ) ( ) ( ) interpunct ( · ) ampersand ( & ) asterisk ( * ) at ( @ ) backslash ( ) bullet ( • ) caret ( ^ ) currency ( ¤ ) ¢, $, €, £, ¥, ₩, ₪ dagger/obelisk ( † ) ( ‡ ) degree ( ° ) dele ( ) emoticons (☻ ) inverted exclamation point ( ¡ ) inverted question mark ( ¿ ) number sign ( # ) numero sign ( № ) percent and related signs ( %, ‰, ‱ ) pilcrow ( ¶ ) prime ( ′ ) section sign ( § ) tilde/swung dash ( ~ ) umlaut/diaeresis ( ¨ ) underscore/understrike ( _ ) vertical/pipe/broken bar ( |, ¦ ) asterism ( ⁂ ) index/fist ( ☞ ) therefore sign ( ∴ ) lozenge ( ◊ ) heart ( ♥ ) interrobang ( ‽ ) irony mark ( ؟ ) reference mark ( ※ ) sarcasm mark Historically, the diaeresis mark or trema is far older than the umlaut mark.
The word trema is taken from the Byzantine Greek τρημα, meaning "perforation, orifice". This sign was first used in that language to indicate a phonological diaeresis, that is when two consecutive vowels are pronounced separately as a hiatus, rather than together in a diphthong. It is currently used with this purpose in several languages of western and southern Europe, among them Occitan, Modern Greek, Catalan, Dutch, and Welsh.
For example, according to the spelling rules of Catalan, the digraphs ei and iu are normally read as diphthongs, [ei̯] and [iu̯]. To indicate exceptions to this rule, a diaeresis mark is placed on the second vowel: without the trema the words veïna [bəˈinə] ("neighbour", feminine) and diürn [diˈurn] ("diurnal") would be read [ˈbei̯nə] and [ˈdiu̯rn], respectively.
Occitan use of diaeresis is very similar to Catalan: ai, ei, oi, au, eu, ou are diphthongs consisting of one syllable but aï, eï, oï, aü, eü, oü are groups consisting of two distinct syllables.
In French, some pairs of vowels that were originally true diphthongs later coalesced into monophthongs, which led to an extension of the value of this diacritic. It often now indicates that the second vowel is to be pronounced separately from the first, rather than merge with it into a single sound. For example, the French words païen [pajɛ̃], Anaïs [anais], and naïve [naiv] would be pronounced [pɛɛ̃], [anɛs], and [nɛv], respectively, without the diaeresis mark, since the digraph ai is pronounced [ɛ].
Another example is the Dutch spelling coëfficiënt, necessary because the digraphs oe and ie normally represent the simple vowels [u] and [i], respectively.
Ÿ is sometimes used in transcribed Greek, where it represents the Greek letter υ (upsilon) in the non-diphthong αυ (alpha upsilon) (e.g., in the transcription Artaÿctes of the Persian name Ἀρταΰκτης at the very end of Herodotus). It also occurs in French as a variant of ï, in rare proper nouns (for instance, the name of the Parisian suburb of L'Haÿ-les-Roses).
In some French words, a diaeresis is used to show what were historically two vowels in hiatus, although the first vowel has since fallen silent. So in "Gaëlle" and in "Saint-Saëns", the diaeresis shows that the combination ae is to read like an e; since the a is silent, the words are pronounced as if written "Guelle" and "Saint-Sens".
As a further extension, other languages began to use the trema whenever they wish to indicate that a vowel should be pronounced separately from the preceding letter (possibly a consonant), with which it would normally form a digraph, according to the orthographic rules of that language. In the orthographies of Spanish, Catalan, Brazilian Portuguese, French, Galician and Occitan, the graphemes gu and qu normally represent a single sound, [g] or [k], before the front vowels e and i (before nearly all vowels in Occitan), for historical reasons. In the few exceptions where the u is pronounced before i or e, a trema is added to it. In French, the diaeresis in such cases is usually written over the following vowel.
Examples:
In Greek it can be used alone (ακαδημαϊκός, "academic"), or in combination with an acute accent (πρωτεΐνη, "protein").

Spanish - vergüenza (shame), pingüino (penguin)
Catalan - aigües (waters), qüestió (matter)
Brazilian Portuguese - cinqüenta (fifty), qüinqüênio (quinquennial)
French - aiguë (acute), "Noël" (Christmas)
Occitan - lingüista (linguist), aqüatic (aquatic) History
The diaeresis mark has also been occasionally applied to English words of Latin origin (e.g., coöperate, reënact), and more rarely in native English words (e.g., noöne), but this usage had become extremely rare by the 1940s. The New Yorker, The Economist, and MIT's Technology Review can be noted as some of the few publications that still spell coöperate with a diaeresis. Its use in English today, apart from words borrowed from other languages, is mostly limited to certain names, such as the surname Brontë and the given names Chloë and Zoë. It is relatively common in words that do not have an obvious divider at the diaeresis point (the diaeresis cannot be replaced by a preceding hyphen), such as naïve.

In English

In Albanian, 'ë' represents a schwa.
ÿ occurs in handwritten Dutch as a glyph variant of the diphthong ij.
Jacaltec, a Mayan dialect, and Malagasy are the only languages to allow a pair of dots over the letter "n", which is presented in unicode as "n̈".
In J. R. R. Tolkien's Romanisation of Elvish names, double dots over trailing e characters (as in Manwë) indicate that the e is pronounced rather than silent, as it would normally be in English. (See Silent E for further information.)
The usage of double dots over vowels, particularly ü, also occurs in the transcription of languages that do not use the Roman alphabet, such as Chinese. For example, 女 (female) is transcribed as nü in proper Mandarin Chinese pinyin, while nv is sometimes used as a replacement for convenience since the letter v is not used in pinyin.
The diaeresis was used in the early Cyrillic alphabet which was used to write Old Church Slavonic. The modern Cyrillic Belarusian and Russian alphabets include the letter yo (Ё, ё), although in modern Russian it is usually printed without the trema (Е, е) unless doing so would create ambiguity. Since the 1870s, the letter yi (Ї, ї) has been used in the Ukrainian alphabet.
The Cyrillic alphabet letters A, O and U (А, О, У) with trema have been used in the Altay, Mari and Keräşen Tatar alphabets for the sounds ä, ö, ü since the 19th century. The Rusyn alphabet uses both Ё and Ї, as well as ÿ for the "ü" sound. In the Udmurt language, the trema is also used with the consonant letters Zhe (Ж, ж → Ӝ, ӝ) and Ze (З, з → Ӟ, ӟ). Umlaut
Historically, the umlaut mark is far younger than the diaeresis mark, and has unrelated origins, though it has been speculated that an awareness of diaeresis might have influenced the final written form of the umlaut.
Originally, phonological umlaut was denoted in written German by adding an e to the affected vowel, either after the vowel or, in small form, above it. (In medieval German manuscripts, other digraphs could also be written using superscripts: in bluome ("flower"), for example, the <o> was frequently placed above the <u>.) In blackletter handwriting as used in German manuscripts of the later Middle Ages, and also in many printed texts of the early modern period, the superscript <e> still had a form which would be recognisable to us as an <e>. However, in the forms of handwriting which emerged in the early modern period (of which Sütterlin is the latest and best known example), the letter <e> had two strong vertical lines, and the superscript <e> looked like two tiny strokes. Gradually these strokes were reduced to dots, and as early as the 16th century we find this handwritten convention being transferred sporadically to printed texts too.
In modern handwriting, the umlaut sometimes looks like a breve, tilde, quotation mark, dash, or other small mark.

History
When typing German, if umlaut letters are not available, the proper way is to replace them with the underlying vowel and a following <e>. So, for example, "Schröder" becomes "Schroeder". As the pronunciation differs greatly between the normal letter and the umlaut, simply omitting the dots is considered incorrect. The result might often be a different word, as in schon 'already', schön 'beautiful' or Mutter 'mother', Mütter 'mothers'.
Despite this, the umlauted letters are not considered part of the alphabet proper. When alphabetically sorting German words, the umlaut is usually treated like the underlying vowel; if two words differ only by an umlaut, the umlauted one comes second, for example:
There is a second system in limited use, mostly for sorting names (colloquially called "telephone directory sorting"), which treats ü like ue, and so on.
Austrian telephone directories insert ö after oz.
In Switzerland, capital umlauts are sometimes printed as digraphs, in other words, <Ae>, <Oe>, <Ue>, instead of <Ä>, <Ö>, <Ü>. (See German alphabet for an elaboration.) This is because the Swiss keyboard contains the French accents on the same buttons as the umlauts (selected by Shift). To write capital umlauts the ¨-key is pressed followed by the capital letter to which the umlaut should apply.

Schon
Schön
Schonen
Schön
Schon
Schonen
Schon
Schonen
Schön Printing conventions in German
Some languages have borrowed some of the forms of the German letters Ä, Ö, or Ü, including Estonian, Finnish, Hungarian, Karelian, the Sami languages, Slovak, Swedish and Turkish. See Turkish alphabet. The use of the diacritic in these languages does not usually relate to instances of the historical phenomenon of Germanic umlaut, but it often indicates sounds similar to those for which it is used in German.
The Estonian alphabet has borrowed <ä>, <ö> and <ü> from German, Swedish and Finnish have <ä> and <ö>, and Slovak has <ä>. In Estonian, Swedish, Finnish and Sami <ä> and <ö> denote [ æ ] and [ ø ] respectively. Hungarian, on the other hand, has <ü>, and <ö>. The Slovak language uses the letter <ä> to denote [ ɛ ] (or a bit archaic but still correct [ æ ]) — the sign is called dve bodky ("two dots"), and the full name of the letter ä is a s dvomi bodkami ("a with two dots"). In all these languages, however, the replacement rule for situations where the umlaut character is not available, is to simply use the underlying unaccented character instead (without a following e).
In Luxembourgish (Lëtzebuergesch), the umlaut diacritic in <ä> and <ë> represents a stressed schwa. Since the Luxembourgish language uses the mark to show stress, it cannot be used to modify the 'u' which therefore has to be 'ue'.
When Turkish switched from the Arabic to the Latin alphabet in 1928 it adopted a number of diacritics borrowed from various languages, including <ü>, which was taken from German (Turkey had a close relationship with Germany) and <ö> from Swedish, which in turn had borrowed this symbol from German. These Turkish graphemes represent similar sounds to their values in German. See Turkish alphabet.
As the borrowed diacritic has lost its relationship to Germanic i-mutation, they are in some languages considered independent graphemes, and cannot be replaced with <ae>, <oe>, or <ue> as in German. In Estonian and Finnish, for example, these latter diphthongs have independent meanings. Even some Germanic languages such as Swedish (which does have a transformation analogous to the German umlaut, called omljud ), treat them as independent letters. In collation, this means they have their own positions in the alphabet, for example at the end ("A–Ö", not "A–Z") as in Swedish and Finnish, which means that the dictionary order is different from German. It also means that the transformations ä → ae and ö → oe are inappropriate for these languages.
Early Volapük used Fraktur a, o and u as different than Antiqua ones. Later, the Fraktur forms were replaced with umlauted vowels.

Borrowing of German umlaut notation
See also: Heavy metal umlaut
The umlaut diacritic can be used in "sensational spellings", for example in advertising, or for other special effects.
As the German short /a/ is more open than the equivalent sound in English (/æ/), Germans sometimes use the diacritic <ä> to imitate the English sound in writing, giving an English "feel" to words used in advertising; in a McDonald's restaurant in Germany one can buy a "Big Mäc".
Since the letter ü is very common in Turkish, its inappropriate use can make a text in another language look "turkified", a purely visual mimicry. Because of the large number of Turks living in Germany, this again is a phenomenon familiar in German. The Turkish-German satirist Osman Engin, for example, wrote a book entitled Dütschlünd, Dütschlünd übür üllüs - the opening line of the first stanza from the Lied der Deutschen, but turkified.
In the heavy metal scene, the umlaut diacritic can frequently be observed as a mere decoration (with no significance for the pronunciation) on the names of bands such as Motörhead, Mötley Crüe, or Leftöver Crack. The fictitious group Spın̈al Tap places an umlaut over the <n>. An interestingly self-referential example is the Finnish group Ümlaut.

Use of the umlaut for special effect
The derivative with respect to time is often represented as a dot above a variable. Two dots represents the second derivative.


This may be contrasted with the more common notation for a derivative using a prime:


In physics, a dot typically represents a (partial) time derivative while a prime represents a spatial derivative .

In mathematics and physics
Most character encodings treat the umlaut and the diaeresis as the same diacritic mark.

Computer usage
It is preferable that umlauts and tremas be available on the keyboard for writing languages that use them. It is rather difficult to use any special key sequences, especially if the character is not considered a modification but an independent grapheme. In practice, the computer must be configured to use an appropriate keyboard layout.
Using Microsoft Word, the double dot is produced by pressing Ctrl+Shift+:, then the letter.
On a computer running Mac OS double dots can be entered be pressing Option+U, followed by the vowel to have a double dot above it.
X-based systems with the Compose key can usually enter characters with double dots by typing Compose, " followed by the letter.
Microsoft Windows allows users to set their US layout keyboard language to Dutch which allows for something similar, by turning keys (rather characters) into dead keys. If the user enters ", nothing will appear on screen, until the user types another character, after which the characters will be merged if possible, or added independently at once if not.
On several operating systems, double dotted characters can be written even without the current keyboard layout having umlauts or tremas by entering Alt codes. On Microsoft Windows keyboard layouts that do not have double dotted characters, one can especially use Windows Alt keycodes. Double dots are then entered by pressing the left Alt key, and entering the full decimal value of the character's position in the Windows code page on the numeric keypad, provided that the compatible code page is used as a system code page. You can also use numbers from Code page 850; these lack a leading 0.

Keyboard input
The ISO 8859-1 character encoding includes the letters ä, ë, ï, ö, ü, and their respective capital forms, as well as ÿ in lower case only, with Ÿ added in the revised edition ISO 8859-15.
Unicode provides the double dot as a combining character U+0308. Mainly for compatibility with older character encodings, dozens of codepoints with letters with double dots are available.
Both the combining character U+0308 and the precombined codepoints can be used as umlaut and as diaeresis.
Sometimes, there's a need to distinguish between the umlaut sign and the diaeresis sign. In these cases, the following recommendation by ISO/IEC JTC 1/SC 2/WG 2 should be followed:

To represent the umlaut use Combining Diaeresis (U+0308)
To represent the diaeresis use Combining Grapheme Joiner (CGJ, U+034F) + Combining Diaeresis (U+0308) Character encodings
In HTML, vowels with double dots can be entered with an entity reference of the form &?uml;, where ? can be any of a, e, i, o, u, y or their majuscule counterparts. With the exception of the uppercase Ÿ, these characters are also available in all of the ISO 8859 character sets and thus have the same codepoints in ISO-8859-1 (-2, -3, -4, -9, -10, -13, -14, -15, -16) and Unicode. The uppercase Ÿ is available in ISO 8859-15 and Unicode, and Unicode provides a number of other letters with double dots as well.


Note: when replacing Umlaut characters with plain ASCII, use ae, oe, etc. for German language, and the simple character replacements for all other languages.


TeX

Double acute accent, a similar-looking diacritic
Diacritic
Dot (diacritic)
Caron
Acute accent
Grave accent
Macron
Tittle
Heavy metal umlaut