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Pippin starts out as the infant of the Fellowship in Book One: he is by far the youngest member, at 28 years old, which in hobbit years makes him around 18. He starts to learn something about fighting and general warrior-ness on the road with Boromir and Aragorn, but he doesn't really start coming into his own until he and Merry are kidnapped by orcs in The Two Towers.
It's on the road with the orcs in The Two Towers that Pippin really starts to show some independence. He'sthe one who has the idea of marking their road so that anyone who might be following their kidnappers will know that Merry and Pippin are still alive. Even so, Pippin is still part of a unit: Merry-and-Pippin. In The Two Towers, he and Merry never seem to separate.
The Return of the King is the first time in the series that we really get to see Pippin Took stand on his own two feet, without Merry to support him. While he misses Merry a ton, of course, he still gets by on his own because he is truly growing up as a person.
Now, let's not get too hasty, here. Just because Pippin is maturing as a character doesn't mean that he has suddenly stopped making mistakes. Of course, the whole reason that he and Merry split up in the first place is because Pippin looks into the palantír at the end of The Two Towers and almost gives away their whole plan to Sauron (accidentally, of course). For his own safety, Gandalf drags Pippin with him to Gondor and leaves Merry with Théoden.
And the mistakes don't end there. At the start of The Return of the King, Pippin arrives at Minas Tirith to meet Denethor, the sneaky Steward of Gondor. Pippin's extreme innocence and lack of self-awareness leads him to spill tons of clues about Boromir's death and about Gandalf's war plans to Denethor without even fully realizing that he has done so.
This talkativeness of Pippin's winds up working in Gandalf's favor, though. Pippin is so straightforward and honest that even tightly wound, suspicious Denethor relaxes a bit around him. Like Théoden with Merry, Denethor takes on Pippin to be part of his fighting force. So, in a surprising twist, Pippin Took winds up a Guard of Minas Tirith. Because above all else, Pippin is lucky. All of his mistakes leading up to this point wind up winning Pippin a position of honor in Gondor (and for the most part helping out the Good Side, too).
Pippin's new job as a Guard of Minas Tirith gives us a view into the lives of the regular folk of Gondor, just like Merry shows us some perspective on the ordinary residents of Rohan. And as usual, Pippin's everyday experiences (while a bit more serious than in the earlier books) are fun to read. They give us a nice change of pace from the usual epic doom-and-gloom talk that covers ninety percent of Gandalf's conversations throughout The Return of the King.
If you're looking for proof of how much Pippin has changed, check out his friendships with Beregond, fellow Guard, and Bergil, Beregond's son. Pippin may still look like a boy to the eyes of a soldier of Gondor, but once Beregond hears about Pippin's adventures, he admits, "you have endured perils and seen marvels that few of our greybeards could boast of" (5.1.125).
Meanwhile, when Bergil tries to tease Pippin (mistaking him for a fellow kid), Pippin warns him, "when you are older, you will learn that folk are not always what they seem; and though you may have taken me for a soft stranger-lad and easy prey, let me warn you: I am not, I am a halfling, hard, bold, and wicked!" (5.1.168). Instead of playing his typical role of the boy getting schooled (usually by Gandalf), now Pippin is the adult schooling another upstart kid. The student has become the master.
Pippin uses his newfound toughness to do two huge things: first, of course, he saves Faramir from burning to death when Denethor tries to set him on fire. Well done, Pippin. And second, Pippin marches into battle at the Gates of Mordor alongside Aragorn and his friends. If you check out his thoughts just before this battle, it's amazing how like Sam's and Merry's they are:
I wish Merry was here," [Pippin] heard himself saying, and quick thoughts raced through his mind, even as he watched the enemy come charging to the assault. "Well, well, now at any rate I understand poor Denethor a little better. We might die together, Merry and I, and since die we must, why not? Well, as he is not here, I hope he'll find an easier end. But now I must do my best." (5.10.55)
Awww. Pippin misses Merry the same way Merry wished for Pippin, way back when Merry was marching off with the Riders of Rohan. Plus, like both Sam and Merry in similarly dire situations, Pippin faces what seem like impossible odds and decides, yep, I'm going to die, but I just have to keep moving anyway. And thanks to Pippin's grace in accepting his fate and continuing on, he manages to kill a mountain troll and he manages to survive. These hobbits are made of tougher mettle than most.
On the other end of the spectrum, you've got Pippin's master, Denethor. When Denethor faces what he believes is certain death, he goes absolutely nuts and tries to kill himself and his injured son. Who knows what might have happened if Denethor hadn't committed suicide? We'll never know if Denethor might have survived the war otherwise. Instead, he dies horribly, without a chance to help his kingdom.
By contrast, while Pippin has come to understand Denethor's despair, Pippin flat out refuses to give up. He does what his other hobbit friends do: he decides that now, he must "do [his] best," even if he might not survive. And he does survive, and goes on to thrive back home in the Shire as Thain (leader) of the Tooks. That pretty much seems to be the lesson of all of the hobbits' adventures: do your duty if you can, do your best even if you fail, and just keep going no matter what, because things may get better. That's a low-key philosophy that we can all get behind.
By now, we've spent literally hundreds of pages reading about hobbits. We know what they look like: on the short side, curly hair, stocky, jolly, with no shoes on their feet because their soles are so thick and tough that they don't need them. Hobbits seem as familiar to us as regular humans do.
But one of the things that's cool about Pippin's adventures in the city of Minas Tirith is that they remind us of how truly unusual hobbits are to people who haven't gotten as used to them as we have. The people of Minas Tirith literally stop in the streets to see Pippin decked out in his Guard uniform, looking like the "Ernil i Pheriannath" (5.1.161) (the "Prince of Halflings").
Pippin stands out on the streets of Gondor because the hobbits are so sheltered from the other folk of Middle-earth. But now, with the adventures of Frodo, Sam, Merry, and Pippin, all of the peoples of Middle-earth are finally starting to recognize the important contributions the hobbits can make to their world. At last, the hobbits are starting to make their mark on Middle-earth, which is yet another sign of how different the world is going to be in the next Age after the fall of Sauron.