I'm absolutely fascinated by cold war history, and I want to read as much as I can about these secret police entities.
I recently read Gulag: A History by Anne Applebaum. Its a Pullitzer prize winner, and a really great read. Though its mostly about the Gulag culture... but its got a lot of history in it as well. Brilliantly written and seriously unputdownable.
Edit: Goodreads link
Sword and the Shield (1992) and The KGB and the Battle for the Third World (2005) by KGB Major Vasili Mitrokhin and Christopher Andrew
The First Directorate: My 32 Years in Intelligence and Espionage Against the West by Oleg Kalugin and Fen Montaigne
Anne Applebaum is really good for this. Not only is there Gulag (mentioned above) but her other great book, Iron Curtain: The Crushing of Eastern Europe, also has a great deal about how the KGB and other Secret Police Forces were used to uphold the Communist regimes in the East. It focuses on Germany (Stasi), Poland (SB) and Hungary (AVH) but mentions all the Eastern Bloc states and is about how the regimes in control kept power and how much influence the Soviets had over them.A very worth while read, if not just to get context on the period.
Another good one more specifically on the KGB's predecessor is "Beria: Stalin's First Lieutenant" which looks at Beria's role in forming the NKVD in the KGB and how they suppressed internal turmoil during the War and in the territories they "liberated". He resigned in 1946 and the book is a biography so it isn't just about his role in the NKVD but it is an interesting read in to the internal suppression of Soviet Union.
Finally I'd recommend two books already listed here. Stasiland gives a great emphasis to real people's stories both from inside and outside the force (but with 1 in 7 people in Berlin connected to the Stasi in the 70s there weren't that many people out side of it) and as well as accounts gives detailed notes on various major events in the period involving the Stasi in someway. The other is Seduced by Secrets - while I haven't read it myself, I know a couple who have a general criticism of it is good (plus some one here has also recommended it so it must be on the right tracks). It's on my personal reading list to finish by the end of next year so I'm looking forward to starting it.
I hope that's helped and that you get all the information you need from this subreddit! Happy New Year! :)
Stasiland is another good one
Seduced by Secrets, by Kristie Macrakis. This book really explores the technology that was used by the Stasi and other totalitarian regimes to spy on and control their citizens.
Stasi, by John O. Koehler. It's well-written, and the author has a first-hand connection to the Stasi, so it's got credibility. It's not as neutral as it could have been, though, so do read it critically.
Also, Killing Hitler, by Roger Moorhouse. This is as readable as Stasi, if not more so, and it doesn't fall into the trap of picking a side that Stasi does. It's primarily about Hitler's would-be assassins, but it also has a strong section on the NKVD and their operations in Germany during the Second World War.
If you ever find yourself in Budapest, check-out the house of terror. It's a museum housed in the former headquarters of two different regimes' secret police. It is terrifying and depressing and fascinating. Really gets into the secret police tactics used by the Nazis and the Arrowcross party, the soviets, and even the stasi
i recommend you to read Aquarium. Aquarium is a partly autobiographical description by Viktor Suvorov of the GRU (Soviet military intelligence directorate).
The Firm: The Inside Story of the Stasi by Gary Bruce is an excellent introduction to the Stasi. Marshall Poe of New Books in History interviewed him for their podcast.
The File: A Personal History by Timothy Garton Ash is also an excellent look at police surveillance from the other side. Ash was a Western student studying in East Germany and The File is his memoir of examining his Stasi file after the Wall came down.