The grappling hook was created by Violet Baudelaire in hopes of saving Sunny Baudelaire from her plight in the birdcage, after Count Olaf dangled her from his forbidden tower and threatened to kill her if she did not comply to be in his play.
In the book, the hook is created using a curtain rod, a piece of wire, and some clothes. Violet manually throws it to the top of the tower and climbs it hand over hand.
In the film, Klaus invents it using an umbrella frame and rope. In the PC and GBA versions of the video game, Klaus makes it using an umbrella frame, shower curtain rings, and a spiral carpet (to unwind it and turn it into rope). In the console version of the game, he makes the "Horrifying Hook" using a bicycle pump, coil, and a gardening hook.
In the TV series, the hook is created using several different supplies including a pasta machine and some curtains. Violet attaches the hook to the tower, and then allows the machine to pull her up.