Shingeki no Kyojin: Lost Girls is a novel compiling the visual novels Mikasa Gaiden: Lost in the Cruel World and Annie Gaiden: Wall Sina, Goodbye. The former was bundled with the first press release of the 3rd Blu-ray volume of the anime's 1st season while the latter was bundled with the 6th volume. The visual novels were supervised by Shingeki no Kyojin's creator Hajime Isayama.
The novel was published in English by Vertical Inc. on June 28, 2016.
First of all, these stories were not written by Hajime Isayama, and like most fanfiction they deviate slightly from the canon's characterisation, having characters say and do things that are out of place yet serve to tell a story. Secondly, if you have watched the first season of the anime (or read that far in the manga) you will understand the context, but otherwise there are huge spoilers that, while also spoiling the original story, may also be very confusing as they are presented without explanation. However I will avoid all spoilers in my review to spare the uninitiated.
Now allow me to break down the
1. Lost in the Cruel World
This is Mikasa's story, and it is a dream of an alternate-timeline set before the fall of wall Maria. Here the theory of the "butterfly effect" is the driving metaphor, so Eren and Mikasa's first meeting as kids is different because of reasons never explained (except through the presence of a butterfly? I suppose we're in dream country now). Eren and Mikasa go on adventures that build their friendship while making nods to the original storyline throughout. The main contention is Armin's familiarity with aeroplanes and his lack of foresight. I imagine the purpose of most alt-universe stories is to show an interesting what-if regarding a story and characters we like -- but here, one is only reminded of why Attack on Titan's plotline was chosen: because it's not BORING.
2. Wall Sina, Goodbye
Annie's story occurs the day prior the the scouting legion's 57th exterior mission into the titan territory of wall Maria. She is now a member of the Military Police, and tomorrow's mission is weighing heavily on her thoughts -- that is until she asks her comrade Hitch Dreyse for a favour and is asked to give one in return, today. The favour is finding a missing woman, Carly Stratmann, the daughter of a merchant company president. This case sends her to the underbelly of wall Sina where drunkards and illicit drug-users run rampant. Of course you can't have an Annie story without some hand-to-hand combat, which this story delivers on a number of times. But as always, there are moments where Annie's characterisation is questionable (like her new-found obsession with donuts turning her into Sasha for a few panels).
3. Lost Girls
The shortest story brings Annie and Mikasa together during combat training when they are recruits. Mikasa confronts Annie about a ring that was dropped after Annie and Eren's sparring. She questions the function of the ring, and then Annie's motivation in joining the military police. There's some tension surrounding what remains unspoken, and the fact that Annie's in the middle of cutting potatoes with a big knife and keeps looking at said knife throughout their conversation.
Overall: these stories happen between events shown in the original Attack on Titan, and provide no speculation on character background or present happenings in the parent story. Even "Lost Girls", which doesn't create an entirely new setting, reiterates knowledge gleaned from the manga and only serves as an opportunity to have these 2 girls talk privately. In that regard they are extremely disappointing. However, the art is wonderful, and if either Annie or Mikasa are your favourite characters it might tickle your fancy.