Set in a seemingly utopian 27th century, Earth society is run by a collection of "electronic brains" (artificial intelligence) called the Great Machine. An early plot point establishes that citizens are to take part in a series of games to attain high-ranking postions and employment. It's while trying to participate in these games that we're introduced to the book's protagonist, Gilbert Gosseyn, who gets accused of pulling a fast one on everybody and gets expelled from the games.
That's when the story starts to take off, as Gosseyn discovers that his memories have been tampered with (shades of Philip K. Dick!), and mysterious characters are either trying to kill him and/or find out why his brain is so..different from other humans'. All these attempts on Gosseyn appear to be connected to some kind of plot involving a takeover of the planet Venus by forces from Earth. Throughout the constant back-and-forth intrigue (Gosseyn encounters more people who aren't what they appear to be than you'd find in a John le Carre novel), what keeps our hero going is his unflinching belief in the "non-Aristotelianist" philosophy of Null-A, which stresses reason and free choice. (It's like Ayn Rand's Objectivism, but without the selfishness.) Eventually, Gosseyn finds out who's behind the whole thing, leading to a stunning (and somewhat overcomplicated) final scene!
Yes, the book betrays it's pulp origins. The writing's not polished, some of the scientific concepts are out of thin air, there's some clumsy segues to scenes and loose ends left hanging, and the less said about the unintentional humor (among the devices Gosseyn uses on his quest is a "vibrator", which isn't what you'd think), the better. Van Vogt's otherwise exciting storytelling skills manage to overcome any stylistic and narrative flaws that the reader comes across, making The World of Null-A (reserve a copy here) a spellbinding and rewarding thriller for any science fiction fan.