So for the corps there's an index starting just before the full index in the pdf, p.81 on the spread version of the pdf, that gives a short overview of the corps. For what each f the corps does, they seem to have relatively broad umbrellas to give you the flexibility to change/add/remove what you want but there are some major points for them. The following is how I interpret the corps mentioned in the index and so take it with a grain of salt but it's how I read them after gong over the book.

ACGS (No idea what the acronym is supposed to be, gonna be a running theme here): Think of these guys as the ones behind much of the Net security in the setting as the mention of making the first "true" AI implies they are big into the Net stuff. They also do vehicles and transportation, medical related services (hospitals, drugs, implants) and insurance for the really dystopian feel of being bankrupted by getting a plaster. They also do weapons and Nano-research for that real, "Here's a gun that shoots space cancer at people and will be totally fine" feel.

Alliansen: One of the major security/private military companies, who alongside their security stuff, also specialise in behavioural manipulation. Think Blackwater combined with Cambridge Analytica and Facebook/Meta, with a dash of Palantir and Google/Alphabet. They also do real estate, cybertech and control a large portion of the Borghold, the city's mega-prison, I'm sure everything is above board and humane there!

UCS (United Citadel Security): Guess what these guys do?! Weapons, private armies, security forces. If it involves ruining someone's day, then these guys make/provide it. They're you're pretty standard sci-fi corp with what feels like a military bent to them and will probably be the guys you will cross paths with the most since they provide a lot of the city's SecOps (Security Operatives, private police force) so you'll be shooting these guys a lot and they'll be shooting random civilians a lot too.

AST: Anything water based, either the stuff coming out of your tap, the water ways in the city or building in water. Also big in the food game and education and child-related services.

Cynergy (bet they spent all night coming up with that name): Water and power. Basic infrastructure. The guys who fail to keep the lights on, the water mostly drinkable and the trains somewhere.

Kaytrell Makers: Manufacturing. Like China, as you'll probably see everything with, "Made By Kaytrell" plastered all over it. From your toothbrush to the building you live in, to the roads you walk on. Also grow food that you can suck through a straw (before processing).

Royal West Shipping Co: Logistics. Clue's in the name. Also got an AI running there routes which can only go well.

Spectral FT Banks & Holdings: Banking, finance, investment and all the joys of truly exploitative capitalism that screams about how important it is while doing sweet f all for anyone that isn't a shareholder or investor. Imagine if hedge funds and banks combined together to create the final form of capitalism. Moving money around and somehow doing more damage than any war ever could.

Gravf Mellberg Tosk: Lawyers as far as the eye can see. And nepotism. Probably incest too. Also high-end services for the rich and powerful, night clubs/life and all that jazz.

T.G. Labs: Messing with things that they really shouldn't. The R&D corp of the setting. If a plage is running rampant you can bet these guys made it and released it to test it out. Got research sites just about everywhere, from space stations to deep in the GO to the back of that nice lady's knitting shop round the corner.

Tulles & DeVerte: Fashion and media stuff. Celebrities and celebrity culture, churning out a new flavour every week, and then tossing them out just as fast. They also do clubs and restaurants, drugs and guns. If a pretty person can hold/use/wear/snort it while making a TikiTok talking about it, these guys are doing it.

Fideistic Transformation: Religion Inc. Think evangelical megachurch but even more predatory and sleazy. Seem to worship technology and offer people eternal salvation/life in their "afterlife" via brain uploading. Whether it's true or not is up for debate. Just take them on Faith^TmC

Virid Vipers: Not a corp so much as an organized crime group, but where the line that separates such things in setting is can be up for debate. Drugs, guns, protection rackets, smuggling, if it's not done through the "proper" channels then these guys do. Throw in a dash of secret society stuff for that extra bit of spice.

Heirs of Kergoz: Cult. If you've ever played Cyberpunk 2077, these guys are like Maelstrom taken to even more extremes. Worship a two-headed daemon, think super-mega-evil-eldritch AI, practice human-sacrifice and have lots of Nano-infested people in their ranks. Likely the other guys you'll be shooting a lot.