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A really interesting history book is The Games that Changed the Game. It's a history of seven football games, each of which altered the course of NFL football. So in each of them, you'll learn how it used to be, and what changed, and why, and how it is today. It's a pretty quick read, well-written, and I think it's a great baseline history of the league.
I really enjoyed The Games That Changed the Game by Ron Jaworski. It discusses how plays or strategies from seven specific games in the past have affected how football is played today.
Most of them are from the 70s and 80s, with the most recent being the gameplan to eliminate Marshall Faulk in Super Bowl XXXVI. It's a good way to start learning football history in manageable bites.
If you want a much better explanation I cannot recommend Ron Jaworski's The Games That Changed The Game enough. It's relatively cheap on Amazon, and your local library probably has a copy as it seems to crop up in the sports sections of a lot of libraries I have visited.
In the most tl;dr fashion I can explain, the Patriots did three things that were key to beating the Rams.
Beat the shit out of their receivers. Destroy the Rams' precision pass game and break up their rhythm. And eliminate Marshall Faulk.
The Patriots were in nickel or dime 80% of the time. They had 5 DBs on the field for 22/69 snaps, 6 DBs for 26/69 snaps, and 7 on 6/69 plays. All told that is 54/69 plays where the Pats had at least 5 DBs on the field, and they used those DBs to jam extensively at the line of scrimmage, and in particular in the five yard zone. This was DEVASTATING to the GSOT Rams, because Warner relied on precision routes that depended on meticulous timing, and they had a hard time adapting when their route timing was thrown off and their receivers struggled to adapt to the Patriots' high-contact coverage. This sort of coverage employed by the Patriots were the primary cause of the 2004 rule changes, intended to make the passing game easier. And it very clearly made the Rams uncomfortable. Even though they beat the Pats in first downs (26-15), total yardage (427-267), total plays (69-54), yards per snap (6.2-4.9) and possession time (33:30-26:30), the Rams bogged down as they crossed midfield, turned the ball over three times, and were uncomfortable on offense throughout the game. The Patriots dared the Rams to run the ball, and the Rams refused to do so. Marshall Faulk only had 17 touches in the game, and was hit, chipped, and knocked off his routes by the Patriots constantly during the game. They hit him even on plays the ball wasn't going to him, and they got in his head early. Faulk never truly got going, and when the piece which made the entire offense sputtered so did the rest of the team.
That Super Bowl XXXVI defense was game-changing.
This book is awesome:
Has a whole chapter dedicated to Belichick
Jaws' "The Games That Changed the Game" is a good read