What does the Cheshire Cat teach Alice? In Alice in Wonderland

The most important thing the Cat does is tell Alice that everyone in Wonderland is crazy - even her. Alice is impressed by the cat's shoot-from-the-hip (or in this case, from the grin!) honesty. Throughout the rest of her adventure in Wonderland, Alice always looks anxiously around her for the Cheshire Cat, hoping for more advice or at least intelligent conversation.