If you bought a Surface that was bundled with a Type Cover or Signature Keyboard, the serial number will be on the barcode label on the box along with the serial number for your Surface.
If you bought a Type Cover or Surface Pro Signature Keyboard separately, the serial number barcode label will be on the box that it came in. If you still have the original packaging, you can find the serial number on the barcode label. The serial number is a string of numbers that looks something like this: Based on this number, it is possilbe to check some information about the device, for instance brand and model, supported bands, operating system and special features. You can find the serial number for your Type Cover near the center or to one side of its spine (the area that attaches to your Surface). Each Microsoft Surface Pro mobile cell phone, PDA or a device with a built-in GSM chipset has a unique 15 digit IMEI number.
Find the serial number on your Surface Type Cover or Surface Pro Signature Keyboard For more info on registering it, see How to register your Surface. Note: Not sure which Type Cover model you have? You can find out when you register it with your Microsoft account.