Vintage Rolex watches have the serial number engraved between the 6:00 lugs. You have to remove the bracelet to see the serial number from the watch.
Mondern Rolex watches have the serial number at the 6:00 position along the inner bezel under the crystal. This style is often referred to as the “inner engraving” or “rehaut engraving”.
The serial number is also listed on the Rolex certificate of your watch.