Trying to fix a leaky faucet, structure was not I expected after removing the knobs
The base in the first photo will unscrew (counterclockwise). It will have to be removed in order to free the faucet base so it can drop through to the bottom. Check the base first for a recessed (set) screw that may keep it from loosening. Set screw can be loosened with a hex or slot driver.  The faucet base may not unscrew easily. In which case you should use either an  adjustable pair of pliers, pipe wrench or vise grip pliers. To prevent damaging the surface of the chrome base you can: wrap the jaws of the pliers with duct tape, wrap a rag around the base or do both.