Arlong Park Arc

Okay so in the previous arc Nami left the crew and went to Arlong who’s basically her boss even though she’s treated as a slave. The crew are now left stranded on the Baratie until they see a rowboat but since Zoro is still recovering Luffy and Sanji leave to Arlong park to find Nami and get their ship back along with their navigator. As they are sailing, they encounter a sea cow which both Luffy and Sanji fight it, and they end up making it take them to the island. when they finally get to the island Zoro and johnny and Johnny tells them that Usopp had been stabbed by Nami but what had actually happened was that she stabbed her hand instead of stabbing her and she just pushed him into the ocean. Luffy shouts at Nami to come back but she chooses not to listen. The villagers start telling the group about namis past but Zoro and Luffy does not listen. A little while later we see that Nami is trying to stop the villagers from attacking arlong to the point where she starts stabbing herself with a knife trying to carve out the arlong symbol, but Luffy stops her.

He then gives her his straw-hat hat and leaves with the group to fight Arlong

in the end Luffy wins the fight between Arlong and the fishmen Pirates and Nami finally joins the Straw-hat Pirates
Lounge Town Arc

after the Battle between Luff and the Arlong pirates the crew heads to the last town before the grand line Lounge Town this is also where Roger the king of pirates was executed. As they are traveling there, we get to see Luffy first Bounty

The crew decides to stop there for supplies. the crew splits up and Luffy goes to the place where the former king of pirates was beheaded where he is then met by Buggy the Clown and Alvida (first pirate he beat) the put him in the execution alter to behead him but lighting strikes his sword and the pirates see it as a sign but all this fighting draws the attention of smoker and the marines who try to capture Luffy. Just as Luffy is beaten by Smoker since he had a sea stone pick which deactivates Devil fruit users Abilities and makes them weak a mysterious man grabs Smoker and lets Luffy get away

the crew gets back together and escape Lounge town and head towards the grand line