I'll give a shot at summarizing things then. One thing the other guy left out was that instead of being a trap to kill a bunch of investigators (or that's what it seemed like in the anime) the purpose of Aogiri Tree taking over the mall was to draw the attention of the CCG and divert as much manpower from the Ghoul Detention Center in the neighboring ward as possible. While the raid was going on the manga reveals that Tatara, Eto, and the main Aogiri force had been raiding the prison, breaking out prominent ghouls like Shachi and Naki.
Instead of joining Aogiri after the Aogiri raid Kaneki makes his own group comprising of Banjo and friends, Tsukiyama, and Hinami. This groups goal is to destroy Aogiri Tree according to Kaneki.
Kaneki and company go through a few different methods to try to figure out Kanou's goals. This includes finding more on Rize's past by backtracing her steps, raiding the ghoul restaurant to acquire Madame A (which fails when they're stopped by the two ghouls who fought Juzuo in the anime), and interrogating one of the nurses at the hospital (which fails when Aogiri Tree shows up with the same goal). Eventually they capture Madame A and get her to take them to the underground facility where Kanou has been performing experiments.
Most of the battles that happen in the Ghoul Detention Center in Root A happen in the manga at this underground facility. Kaneki leaves Tsukiyama/Banjo to deal with Naki and his goons. They end up teaming up when the CCG shows up.
Kaneki fights Shachi who ends up beating him. Before their fight can conclude Dr. Kanou shows up, reveals Rize is still alive and has been the unwilling ghoul donor for his experiments. He then joins Aogiri Tree willingly, inviting Kaneki to join him. Yomo appears, takes Rize, and tells Kaneki to walk his own path.
Shachi leaves with Kanou. Kaneki goes Kanekipede on Kanou's failed experiments which are released to stall him as Kanou leaves. Shinohara's squad appears and fights Kaneki. Instead of being saved by Eto he retreats on his own due to character development that I won't explain here because that's another novel on it's own. But it's sparked during Amon's battle with Kaneki after the latter beats Shinohara.
Kaneki and friends withdraw and after learning of Yoshimura's relation with Eto Kaneki asks to disband his group and invites all except Tsukiyama to return with him to Anteiku.
While in a cafe before returning Kaneki hears two investigators discussing the upcoming raid on the 20th ward's owl. Kaneki warns Yomo who warns Yoshimura. At this point we're back at the point of the anime, with Kaneki rushing to reach Anteiku. The only difference as of episode 9 regarding the Anteiku raid only is that Yomo stops Touka instead of letting her go.
Sorry about the length. I tried to cut it down without leaving out too much context, and still showing what changed and remained the same between anime and manga. A lot more happens in the manga than in Root A. I left a lot out and summarized chapters worth of development into single sentences up there.