The best part of this book is the in-depth explanation of the Fate Accelerated approaches. One place where people new to Accelerated trip up is thinking that approaches work like stats in other games, or even like skills in Fate Core or other games. How these things work is right there on the tin: approaches. Keeping in mind that approaches are how a character approaches a game situation can make them much less frustrating, and unlock the key to their simplicity and flexibility. It is the approaches where Fate Accelerated really sings, and where a lot of the game's streamlining is happening. A lot is packed into a little space with approaches.
For those who might be new to Fate Accelerated, the Accelerated Book of Approaches also offers some new approaches inspired by the attributes from various open gaming licence systems like D6, D20 and Mongoose's Traveller rules. This highlights the flexibility and hackability of Fate Accelerated by introducing new approaches that can help familiarize a new game by introducing elements that players may already understand from other games. For me, this is a strength of the Open Gaming License, and I would like to see more publishers bring bits and pieces back and forth from various licensed systems to make new things.
However, to be honest, the adaptations in this book are not as interesting as they could be. I think that sample characters could have better demonstrated these adapted approaches. That isn't to say that these approaches wouldn't work, just that they aren't as flavorful and as interesting as they could be.
Before you give up on the Accelerated Book of Approaches we haven't actually gotten to the best part: the sets of brand new approaches. There are three sets of original approaches for "Action"-oriented games, games set in "wizarding schools" and also for "space knight" campaigns. The Action approaches are interesting, and could work well for a pulp-based Fate Accelerated game, or one inspired by the television show Leverage. The Wizarding School approaches are obviously inspired by the Harry Potter books/movies, however these approaches could be used for any sort of wizard-oriented campaign where everyone is a spell-caster of some sort. A creative GM could build an Ars Magica Acclerated hack off of these approaches. The Space Knights approaches look like they are inspired by the "force powers" from the original West End Games Star Wars RPG, which is an interesting...approach.
Like I said, this book is a starting point for people using Fate Accelerated in their games. There is still going to have to be some lifting on the part of the GM to explain these approaches in a game, and to figure out the situational applications of some of them. People interested in a D&D Accelerated game should also look at the Freeport Companion that Evil Hat and Green Ronin put out. While that is a supplement for Fate Core, it could easily be hacked for use with Fate Accelerated. It also has some interesting stuff for anyone looking to do D&Dish gaming using any version of the Fate rules.
This PDF is all starting point. The GM of an Interstellar Patrol game is going to have to understand the genre of Star Trek and how it is different from other types of science fiction. However, as a Pay What You Want PDF you can pick it up for free. I do think it is worth a dollar (at the least) for giving GMs a starting point. The cover is pretty cool as well.
With this PDF and the Fate Accelerated rules you can pick up and play a fast game on one of those nights when not everyone is able to show up for game night but you still want to play a game. That quickness and simplicity of Fate Accelerated is another one of the many strengths of the system.
I recommend both, or either of these two supplements for Fate Accelerated. Hopefully they will be successful enough to encourage more simple and low cost plug-ins for the game.