What is the plot connection between Infernal Affairs 1, 2 and 3?

Actually, there is one in the middle. The second part is about Andy Lau and Tony Leung when they debuted when they were young. The third part follows the first one, and some of the time is consistent with the first one. Yes, but it is generally about what happened after Tony Leung died.

Infernal Affairs 1 plot synopsis:

Two men with confused identities, they are undercover agents of the police and the underworld respectively. Now they are determined to leave this situation where they cannot distinguish right from wrong, leave the endless hell, and find themselves. Liu Jianming (played by Andy Lau) is a member of the Hong Kong gangster triad. More than 10 years ago, he followed the instructions of the boss Han Chen (played by Eric Tsang) and joined the Hong Kong police to work as an undercover gangster.

With Han Chen’s help, Jianming is expected to be promoted to a trainee inspector in seven years. This is a big official! Chen Yongren (played by Tony Leung) originally wanted to be a good policeman, but was forcibly dropped out of the police training school and secretly performed undercover work to infiltrate the Three Peace Conference. He is now a popular figure in the gang, and his boss happens to be Han Chen. In a drug deal, both black and white operations failed. The fact that there are undercover agents on both sides is revealed, and the Infernal Affairs journey of Chen Yongren and Liu Jianming will undergo a severe test.