How does Jim, the narrator in Treasure Island, mature over time?

Jim Hawkins experiences a profound transformation over the course of Treasure Island. He starts the book as a boy but ends it as a man, having experienced enough adventure to last several lifetimes. But the growing-up process for Jim starts before he even sets foot on board ship. After the sudden death of his father, huge responsibilities are placed on his young shoulders. Not only does he have to arrange his father's funeral, he also has to take over the running of the Admiral Benbow.
No sooner has Jim been plunged headlong into the adult world than he's faced with an even bigger challenge—escaping Bones's enemies and making off with a chest full of loot and a treasure map. Whether he likes it or not, Jim's now responsible for his own destiny in a way that no child should ever have to be. His father's dead, and now he's had to hide his mother for her own protection. And that's before his escapades on the high seas have even started.
Once on board ship, Jim continues to grow up fast. He senses that appearances can be deceptive and that Long John Silver's back-slapping bonhomie hides a deeply manipulative personality. Yet even though Jim's figured out Silver pretty quickly, even though he knows just how dangerous he can be, he still doesn't hesitate in spying on him for Smollett and Trelawney. Jim also witnesses acts of theft and murder and overhears information that provides him with insight into how adults think and behave.
As the story progresses, Jim starts to take more responsibility for his actions. He finally comes to accept that he is in control of his own fate, even in a harsh, brutal world full of cutthroat pirates and thieves. On his own initiative, he boards the Hispaniola to take it back, fighting off Israel Hands in the process. This is the point in the story when we can say, without a doubt, that Jim Hawkins has achieved full maturity.