The original trilogy. Originally released in Japanese for PC then ported to PSP/PS3. All of them were localized in Chinese for PC (The Chinese company Joyland also developed on their own PC versions in Chinese for Ys Seven and Ys Celceta - as well as a brand new spinoff on PC for the Trails series). All licensed by Xseed, one released, another announced for English release. No other European language localizations.
Sora no Kiseki / Trails in the Sky: available in English (PC, PSP)
Sora no Kiseki SC (Second Chapter): announced for a 2014/2015 English PSP/PC release.
Sora no Kiseki 3rd: Xseed licensed it, no announcement.
The following games were never licensed for Western release, and are sequels for the previous games. They were made originally for PSP, then got an enhanced Vita version. The Chinese company Joyland ported them to PC on their own (as opposed to the original trilogy being developed in-house by Falcom for PC). Falcom released a Japanese version of Zero no Kiseki PC that flopped hard - they announced they were dropping their future PC endeavors as a result.
For what it's worth, Zero no Kiseki has an ongoing fan-translation effort.
Zero no Kiseki
Ao no Kiseki
Another sequel series, for PS3 and Vita (no PC). Sony Asia is making an Asian version including Chinese and Korean localizations (the Japanese-language releases of the previous games were very popular in Korea):
Sen no Kiseki
Sen no Kiseki 2
And there's the spin-offs. Won't be localized (pretty much confirmed since Xseed dropped PSP support, and Falcom has an exclusivity contract with them, and Xseed's ties with Vic Ireland -who's still looking into the platform- aren't the best due to a nasty incident involving a DS re-release of one of their localizations):
Ys Vs. Sora no Kiseki
Nayuta no Kiseki
The Trails/Kiseki series are part of a larger series, The Legend of Heroes, that has been around since 1987. It was predated by the Gagharv trilogy which was indeed localized on PSP in English by Namco (with the order messed up :/ ). Sadly it doesn't even compare to the greatness of the Trails series, and to add insult to injuries has an awful translation.
tl;dr: so, you have a series with 7 massive interconnected episodes, only the first was translated, and you jumped from episode 1 to episode 5 which you're playing untranslated? You can't really play through this series out of order.