Do you have any recommendations for fantasy and/or science fiction written by women? Especially multi-installment series?
First and foremost: Lois McMaster Bujold, one of my favorite authors of all time. My favorite series of hers will always be her Vorkosigan Saga (see my guide to reading order). But I also especially love her Chalion series, which I think would very much appeal to fans of ASOIAF (some reccing of it here). There’s also her Sharing Knife series, which I don’t consider a favorite, but is still very good and has a lovely romantic story (you can read the first few chapters here). She also has a solo novel or two that are rather good.
Another author I like is Naomi Novik, and her Temeraire series. I rec it here, along with some other series. You like dragons, these are the books for you.
I haven’t read that much Connie Willis, but she’s excellent (she’s the #1 winner of sf awards for a reason). Her time travel novels are not exactly a series as such, but share some characters and setting. (I may never read Doomsday Book again, though — it was very good, but way too depressing for me.)
Diane Duane is one of my favorite Star Trek writers ever. Her stories of the Romulans are considered by fans to be more canon than actual canon. ;) She also has an excellent YA series, Young Wizards, which I’m terribly behind on (I’ve only read like the first two books ages ago), but I know has a fiercely devoted fandom. And I know she has other series too, they’re probably all quite good.
Other female sf/fantasy authors I like… hmm, Jody Lynn Nye, and her Mythology 101 series; and Esther Friesner, who had multiple series that are probably out of print now but I loved in the 90s — she also edited the Chicks in Chainmail anthology series, which featured (mostly) women authors and female protagonists; and all the women authors involved in the Thieves’ World series (including Diane Duane, whose characters were my favorites).
And of course there are certain rather famous female sf/fantasy authors that I like, but who don’t need me to rec them, I’m sure. :)