Are you just gonna casually use the phrase "hentaigana" and not explain what it means to uncultured swine like myself?
sorry, i previously mentioned hentaigana precisely two times on this webbed site so i thought everyone would be up to speed
but seriously, in a nutshell, hentaigana are non-standard hiragana, and there's a decent enough wikipedia article on them here. up until the 19th century (inclusive), it was common to see hiragana written and printed in multiple ways. All hiragana are highly cursive forms of kanji that have a similar sound to the intended syllable, and hentaigana are either cursive forms of different kanji to the "standard" hiragana, or based on the same kanji as "standard" hiragana but written in a different cursive style.
Here's an example: the current standard hiragana for the sound ka is か, and this comes from the kanji 加 which can also be read as ka. There are other hentaigana for the sound ka: 𛀙 (the rightmost form in the "hiragana" row in the image above) which comes from the kanji 可 (also read ka), and 𛀘 (the guy in the middle of the "hiragana" row above) which is a slightly different cursive form of 加. these hentaigana might not display on your screen (they don't display on my screen as I'm writing this!!) so have a look at the figure above to see what i mean. The hiragana marked with red boxes are hentaigana.
that's the basic overview but there's more below if you want to go deeper
because hentaigana can be derived from the same kanji as regular hiragana, it is often difficult to decide whether any particular premodern handwritten form is just a slightly different way to write the same hiragana form, or whether it should be classified as a separate variant form. this can make it tricky to research the history of these critters in a quantitative way. i gave it a shot myself, though, and i found out (or rather, i used data to confirm a passing comment in an earlier paper) that printed books basically stopped using hentaigana across the board around 1890 CE.
children were not taught all the hentaigana in one go. in fact at one point in history, children started learning katakana before any hiragana (in modern schools they teach hiragana first). but anyway, this is kind of outside of the period i studied, but historically when children were taught hiragana, they typically copied the iroha poem (a pangram with all the kana. there's an interesting little history of japanese pangrams. this post is already long enough but here's a little bit: the wiki page linked earlier has a link to an earlier pangram called ametsuchi no uta which happens to have more syllables than the iroha poem, because there were a few extra types of sounds within Japanese at the time that later dropped out) which has one hiragana per syllable. it is also almost exactly the same as the modern set of standard hiragana, but with a few exceptions for o, so, and e, as well as the now generally unused wi ゐ and we ゑ (unused because there is no distinction in sound for these two syllables within the modern-day language, though they are used for effect).
the earliest use of the term hentaigana that I know of goes back to 1877 and these variant forms are also called itaigana 異体仮名 and confusingly man'yogana 万葉仮名. I say "confusingly," because the term man'yogana is currently used in research to refer to the use of (relatively) non-cursive kanji to write japanese syllables (as found in the man'yoshu anthology of poems)
oh i should mention that the hentai in hentaigana is written in kanji as 変体, which basically means "variant forms," and it is not the same as the hentai (変態) that is the english word for ero-manga and ero-anime.
