Ryakuji

Use

Ryakuji are primarily used in individual memos, notes and other such forms of handwriting. They have declined in use in recent years, possibly due to the emergence of computer technology and advanced input methods that allow equally fast input of both simple and complex characters. Despite this, the ryakuji for 門 (mon, kado; gate [also a radical, mongamae]) is still widely used in handwriting.
In all case discussed in this article, individual characters are simplified, but separate characters are not merged. There are rare cases of single-character abbreviations for multiple-character words or phrases, such as 圕 for 圖書館, 図書館 toshokan, "library", but this is very unusual; see polysyllabic Chinese characters for this phenomenon in Chinese, where it is more common.

Further examples

Omitting components is a general principle, and the resulting character is often not a standard character, as in 傘→仐.
If the resulting character is a standard character with the same reading (common if keeping the phonetic), this is properly kakikae instead, but if it is simply a graphic simplification (with a different reading) or the resulting character is not standard, this is ryakuji. One of the most common examples is 巾 for 幅 haba "width". Often the result would be ambiguous in isolation, but is understandable from context, as in 国→囗. This is particularly common in familiar compounds, such as 齢→令 in 年齢→年令, 歴→厂 in 歴史→厂史, or 経→圣 in 経済→圣済.
In some cases, a component has been simplified when part of other characters, but has not been simplified in isolation, or has been simplified in some characters but not others. In that case, simplifying it in isolation can be used as common ryakuji. For example, 卒 is used in isolation, but in compounds has been simplified to 卆, such as 醉 to 酔. Using 卆 in isolation, such as when writing 新卒 shin-sotsu "newly graduated" as 新卆, is unofficial ryakuji. As another example, 專 has been simplified to 云 in some characters, such as 傳 to 伝, but only to 専 in isolation or other characters. Thus simplifying the 専 in 薄 (bottom part 溥) to 云 is found in ryakuji.
More unusual examples come from calligraphic abbreviations, or more formally from printed forms of calligraphic forms: a standard character is first written in a calligraphic (草書, grass script) form, then this is converted back to print script (楷書) in a simplified form. This is the same principle as graphical simplifications such as 學→学, and of various simplifications above, such as 第→㐧. A conspicuous informal example is 喜→㐂 (3 copies of the character for 7: 七), which is rather frequently seen on store signs. Other examples include 鹿→𢈘; and replacing the center of 風 with two 丶, as in the bottom of 冬. 御 has various such simplifications. In Niigata (新潟), the second character 潟 is rare and complex, and is thus simplified as 潟→泻（氵写）.

Derived characters

Derived characters accordingly also have derived ryakuji, as in these characters derived from 門:
Similarly, the 魚→𩵋 simplification is often used in fish compounds, such as 鮨 sushi, particularly in signs.

Phonetic simplifications

Some ryakuji are simplified phono-semantic characters, retaining a radical as semantic and replacing the rest of the character with a katakana phonetic for the on reading, e.g., 議 (20 strokes) may be simplified as 言 (semantic) + ギ (phonetic gi for on reading):
Another example is 層 sō, replacing the 曽 by ソ so.
This may also be done using Latin characters; for example, the character 憲 (as used in 憲法 kenpō, "constitution") may be simplified to "宀K": the radical 宀 placed over the letter K; this is particularly common in law school. Similarly, 慶應 (Keiō) as in Keio University may be simplified to "广K广O": the letters K and O respectively placed inside the radical 广. In this case the pronunciation of "KO" (as an initialism) sounds like the actual name "Keiō", hence the use.
The character 機 has a number of ryakuji, as it is a commonly used character with many strokes (16 strokes); in addition to the above phono-semantic simplification, it also has a number of purely graphical simplifications: