I promised y'all a thread on female teachers of Torah throughout history. Here it is, neither comprehensive nor complete.
So not really teachers of Torah, but in my tradition, there are 7 women prophets in the Hebrew Bible: Sarah, Miriam, Deborah. Hannah, Abigail, Huldah, and Esther. Obviously there were many strong, kickass women in the Bible (shoutout to Judith, Yael, Tamar, many others).
As we get into the early Rabbinic world, Bruria was the wife of Rabbi Meir and respected as a teacher of Torah in her own right (and prodigious--said to have learned 300 laws on a single cloudy day)

https://en.wikipedia.org/wiki/Bruriah 
Oh, back to the Bible, have to name Mahlah, Noa, Hoglah, Milcah, and Tirzah, who, again, didn't teach Torah in any traditional sense but did challenge patriarchal inheritance laws and forced a change in them.

https://en.wikipedia.org/wiki/Daughters_of_Zelophehad
Moving on, not necessarily in historical order: Asenath Barzani, (1590–1670), a Kurdish Jewish woman living in Iraq who was a great scholar of Kabbalah and other trad texts, head of a yeshiva, and given the title Tanna’it. https://en.wikipedia.org/wiki/Asenath_Barzani Beautiful drawing by @RiffChick
A couple of sofrot/scribes, not teachers of Torah per se but part of the larger story-- Paula Dei Mansi of Italy (13th c.) https://en.wikipedia.org/wiki/Paula_Dei_Mansi
It's said that Rashi's daughters (11th-12c. France), Rachel, Yocheved and Miriam, were very learned in Torah and Talmud and lay tefillin. It's more established that his granddaughter Hannah taught Jewish law relevant to women.

https://en.wikipedia.org/wiki/Rashi%27s_daughters
The Baal Shem Tov had a daughter named Aidel (b. 1720, Ukraine) said to have great powers. After her father’s death, she was known as a rebbe who received male guests from behind a screen to whom she gave blessings, advice and handed out Kabbalistic amulets.
Ray Frank (1861-1948), known as "the Girl Rabbi of the Golden West" when she taught and preached up and down the West Coast: https://en.wikipedia.org/wiki/Ray_Frank 
Puah Rakovsky (b. 1865 Poland, d. 1955 Israel) founded a Jewish school for girls, was the fictionalized heroine of a novella ("Rabbi Shifra" by Ben-Avigdor), worked for women's civic & political equality, equal pay, education, self-id'd as revolutionary: https://jwa.org/encyclopedia/article/Rakovsky-Puah
Lily Montagu (1873-1963 England) was a force in Liberal/Progressive (Reform) Judaism, writing about spirituality, leading prayer, preaching, as well as founding synagogues and organizations, was President of the World Union for Progressive Judaism: https://jwa.org/encyclopedia/article/montagu-lily
Regina Jonas (1902-1944, Germany), known as the 1st woman to be ordained as a rabbi--in 1935 through the Liberal (Reform) movement. She continued to work & teach in Theresienstadt, incl much pastoral work to prevent suicide. She was murdered in Auschwitz.
https://en.wikipedia.org/wiki/Regina_Jonas
In 1972 Rabbi Sally Priesand was ordained in the American Reform movement. In 1984, Rabbi Amy Eilberg was ordained in the Conservative movement. A few women were ordained privately by Orthodox rabbis over a few decades; Rabba Sara Hurwitz' 2009 ordaination paved the way for more.
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