Horatio Hornblower. In space. And female.
I read books 1-6 in quick succession so this is a combined review of them all.
The author creates a believable universe in which FTL travel occurs in a manner that, through necessity, replicates the feel of the age of sail of the early 19th century. While this might seem contrived at first glance, this reality is so interwoven into the characters and the universe that you quickly just accept it as (fictional) fact and enjoy the story. The technology levels of developed worlds hits all of the expected high notes; it is really just the FTL travel that morphs into a different era.
The tale of Alexis Carew mirrors that of Horatio Hornblower to a great extent. Born into a star-spanning nation modeled politically and culturally on the British Empire of the early 19th century, Alexis joins the Navy as a midshipman and faces a series of trials and adventures that certainly pay homage to, and remind the reader of Hornblower's travails. Carew's tale includes more of her home life than Hornblowers, which adds to and deepens her journey, rather than distracting from it.
As one would expect, her gender is an area of conflict on multiple occasions, but is not overdone or used as a blunt instrument.
The books are PG-13, with occasional detailed violence, some allusions to sexual activity, and some language, though most of that uses 19th century terms. If you are proficient in German or French, the language does get more explicit. Overall, though, the reader is protected by a veneer of class that keeps the story from being overly gritty and is in keeping with a series that, at its core, starts with the journey of a 15 year old girl.
Overall, I highly recommend the series. At its core, it is a YA/NA series with a strong female lead, strong character growth and a plot that includes not only adventure, but intrigue and romance as well.