True Love
True love is the catalyst that sets the entire plot of The Princess Bride in motion. Westley and Buttercup share a love as passionate as any that came before it. When they're separated, Buttercup's love for Westley leads her to swear she'll never love again, while also tying her to him through his promise that he will always come for her. True love is what motivates Westley to rescue Buttercup on multiple occasions, and is the noble cause that (partially) inspires Max to bring Westley back to life. Westley's repeated phrase, "As you wish," is meant to signify how much he loves Buttercup, and the line takes on an even greater meaning when the grandfather employs it at the very end of the film, communicating his love for his grandson the same way Westley communicates his love for Buttercup.
Revenge
As with true love and pain, revenge serves as an important motive for several of the characters' actions in the film. Most prominently, Inigo Montoya has dedicated his life to exacting revenge on the man who killed his father, spending countless hours studying fencing to prepare for a swordfight with the man. He is so consumed by vengeance that once Count Rugen is dead, he confesses himself at a loss for what to do next, though Westley is quick to offer him the position of the Dread Pirate Roberts. Prince Humperdinck is also an agent of revenge: he hopes to use revenge as an excuse to declare war on Guilder, despite being the perpetrator of the crime he will cite as his motivation. He subjects Westley to the maximum torture possible on The Machine as revenge for how Buttercup makes him feel shameful and inferior. However, whereas Westley could have justifiably killed Humperdinck and kept the favor of the viewer, he chooses instead to spare his life, demonstrating how he differs from his antagonizing counterpart by breaking the cycle of you-wrong-me-I-wrong-you.
Politeness
In keeping with the idea that nothing in the story should be taken too seriously, The Princess Bride has its characters be exceedingly polite to one another even at their greatest moments of tension. This is perhaps best exemplified during Westley's conquering of Buttercup's three captors: first Inigo allows Westley sufficient time to rest before they begin their duel, during which time he exposits the reasons for his vengeful fencing training—in this way, politeness is used to allow us to understand Inigo's character and motives. They then continue to exchange pleasantries as they duel. Westley similarly engages in cordial small talk with Fezzik, even as the latter attempts to punch him, and as he eventually chokes him unconscious. And Westley displays considerable restraint and good manners when faced with Vizzini's arrogant antagonism and battle of wits. The underlying purpose of all this politeness is to maintain the comedy of the film even in seemingly serious moments, and more broadly to keep the audience relaxed and enjoying themselves despite the conflict onscreen.
Pain
In a story predicated on love, loss, and revenge, it's perhaps no surprise that pain is used both as tool for character development and a plot device throughout the film. Buttercup's pain at believing Westley to be dead is part of what resigns her to agree to marry Prince Humperdinck, as well as to take her daily horse rides through the country as a means of comfort and escape. Westley's pain at thinking Buttercup betrayed him is what causes him to hide his identity from her for so long (and leads to a very memorable line: "Life is pain, Highness. Anyone who says differently is selling something."); Humperdinck's pain when Buttercup shames and taunts him is what leads him to torture Westely nearly to death; Westley's pain in the Pit of Despair is literally what called Inigo and Fezzik to him; and Count Rugen's desire to study and write a book about pain by torturing captives is a part of what defines him as such a sinister villain.
Deception
The Princess Bride would be nothing without the story's many instances of false identities and lies. Buttercup's entire connection to Humperdinck is built on deception, as he claims to love her while actually planning to use her to frame Guilder for murder and begin a war. Vizzini, Inigo, and Fezzik briefly pretend to be circus performers; the man in black pretends not to be Westley for a great deal of time after he's saved Buttercup (and indeed, his entire persona as the Dread Pirate Roberts is a lie since the real Roberts has been retired for 15 years); and Fezzik pretends to be a ghostly version of the Dread Pirate Roberts to help them gain access to the castle. One could even argue that the novel The Princess Bride within the film is itself a tool of deception since it's claimed to have been written by S. Morgenstern, who in reality is a fictional author made up by William Goldman.
Rescues
As with any classic damsel-in-distress story, The Princess Bride is full of daring rescues that come in many forms. Of course, there are the several different quests to save Buttercup: first from Vizzini and his men; then from the man in black as Humperdinck pursues them; then from the dangers of the Fire Swamp, as Buttercup's dress catches on fire, she is sucked into lightning sand, and then attacked by the ROUS's; and of course, from marrying Humperdinck himself. The film also boasts several other rescue narratives not related to her, though. For example, Fezzik saves Inigo from the Brute Squad; they rescue Westley from the Pit of Despair; and Miracle Max rescues Westley from certain death. All of these narratives fall into the common formula of antagonist-causes-problem-protagonist(s)-undoes-problem. And of course, there are moments when we the audience are rescued thanks to the framing story: when Buttercup is about to be eaten by an eel, the beast lunges at the camera, momentarily scaring us before we are sucked back into the bedroom where the story is being read, saving us from the fear and tension of the previous moment and reminding us that we are safe so long as we ground ourselves in reality and don't get lost in the tale.
A Story Within a Story
One of the defining features of The Princess Bride is that the story of Westley, Buttercup, Inigo, et al. is framed by the story of an unnamed grandfather reading a book, which is the source of the story we hear, to his grandson. Not only does this serve to break tension and offer comedic relief at the writer's whim by pulling us from the world of the story-within-a-story back to the bedroom, it also helps the reader remember not to take the events unfolding so seriously (after all, it's only a story). This helps parallel the viewer's experience with the boy's as they, like him, become so enthralled in the narrative that they need a gentle reminder to lighten up and simply enjoy the adventure.