The title histories during the Invasion

Champions as of the start date which I will go with KOTR 2001 as that's when Booker T arrived and the angle started in earnest the next night on Raw. This was 6/24/01. The angle officially ended 11/18/01.
WWF Champion: Steve Austin to Kurt Angle to Steve Austin
WWF IC Champion: Kane to Albert to Edge to Lance Storm to Edge to Christian to Edge to Test to Edge
WWF European Champion: Matt Hardy to Hurricane to Bradshaw to Christian
WWF Hardcore Champion: Test to Rhyno to Mike Awesome to Jeff Hardy to RVD to Jeff Hardy to RVD to Kurt Angle to RVD
WWF Light Heavyweight Champion: Jeff Hardy to X-Pac to Tajiri to X-Pac
WWF Tag Team Champions: Dudley Boys to APA to DDP/Kanyon to Kane/Taker to Dudleys to Jericho/Rock to Test/Booker to Hardys to Dudleys
WCW Champion: Booker T to Kurt Angle to Booker T to The Rock to Chris Jericho to The Rock
WCW US Champion: Booker T to Kanyon to Tajiri to Rhyno to Kurt Angle to Edge
WCW Tag Team Champions: Palumbo and O'Haire to Kane/Taker to Booker/Test to Hardys to Dudleys
WCW Cruiserweight Champion: Shane Helms to Kidman to X-Pac to Kidman to Tajiri
At the end of the angle, the US/IC and tag titles were unified, the WWF LHW title got retired and WWF took the Cruiserweight title which was retired in 2007 and revived in 2016 (in name only, it doesn't share the title lineage), and the WCW Championship was renamed the World Championship. In December 2001, the WWF and World Championships were unified into the Undisputed Championship which then became the WWE Undisputed Championship and then WWE Championship. In 2003, the US title was revived for Smackdown, and the WCW/World Championship was revived on Raw as the World Heavyweight Championship with the Big Gold Belt but technically a new lineage. New tag titles were brought up but had no linage to the WCW Championship. Also in 2002, the IC and European Championships were unified, which was then unified with the Hardcore Championship, which was finally unified with the World Heavyweight Championship. The IC title was revived in 2003, and the WHC would go on to be unified with the WWE Championship in 2014 to be known as the WWE World Heavyweight Championship, which then became the WWE World Championship in 2016 when the WWE Universal Championship was created for the second brand split.

Oh and the set up for the unification matches was Commissioner Mick Foley coming out and SHEWTING on how he's barely been used because Vince came back right after he was made commissioner, so fuck Vince, and there are so many fucking titles that mean nothing and if you don't have a title there must be something wrong with you because when he was champion, titles still meant something. He's bitter as fuck and berries the angle, the titles, a random shot at X-Pac, Vince, and the writing team. I believe he quits or is fired on the Raw after Survivor Series but I don't remember exactly. He also got some stuff wrong so JR and Heyman shit on him for having brain damage.