Interesting, this. So far in Dark Heresy the focus has been on maintaining religious purity rather than law and order, albeit the two get a bit blurred in an undemocratic empire where the head of state claims godhood. Here, however, is a glimpse of real law enforcement, and how it is conducted within the Imperium (or at least, in the Calixis Sector) by the Arbitrators of the Adeptus Arbites. If investigations and mysteries feature large in your games, this is a resource worth reading.
First up, Chapter 1: Calixian Law discusses the work of the Arbitrators in the Calixian Sector, including some of the notable individuals involved. Their role is to uphold and maintain Imperial Law - the galaxy-spanning Dictates Imperialis - which seems to serve the Imperium much more than it does its citizens. Meanwhile, local Enforcers attend to more mundane matters such as murders and theft according to the laws laid out by each individual planet. There's a lot here from recruitment and organisation to methods, quite enough to let you bring them alive whenever the party encounters them. The other side of the coin is here as well, the Calixian Underworld.
Then, Chapter 2: Bound to Law is full of character options on both sides of the law: Arbitrators and Scum. Useful for building NPCs as needed, it may also offer interesting side careers for existing characters or bring something unusual into the party.
Next, Chapter 3: Arbites Armoury is the 'gear chapter', with all the kit an Arbitrator might want as he goes about his business. Here you will find melee and ranged weapons, armour, utility items, cyber-mastiffs and servitors, along with drugs and cybernetics. The cyber-mastiffs and other creations are an invaluable aid to the dedicated enforcer of the law.
This is followed by Chapter 4: Investigation. Mainly intended for the GM, it explains how to create investigative adventures and run them to effect. It goes through the process in detail, from introducing the investigation into the game, the elements of an investigation, weaving events into the story, finding clues, bringing in complications, and the all-important wrapping it up at the end. It mixes ideas and concepts seamlessly with game mechanics, and provides a solid base upon which to construct your own adventures of this nature.
Chapter 5: Calixian Most Wanted then introduces a rogues gallery of notorious criminals and some of the crimes that they have committed. It also presents a dark settlement, Hive Subrique, currently languishing under martial rule - which is doing nothing to deter the criminal underbelly of the place, however!
Finally, Chapter 6: Jurisdiction is a complete ready-to-play adventure that will take a ready wit to unravel. When a smuggler and general rogue is allied with a Bishop, things tend to get messy...
This book puts a lot of context into the game, and is is worth reading as background to the rich panolply of the 41st century Imperium even if you are less enamoured of investigation-based adventures. If you do like them, waste no time in adding it to your shelves... and the adventure is fun and convoluted and may even convert those who normally avoid investigations into individuals with a keen nose for a mystery.