Further and farther are often used interchangeably, although they actually have slightly different meanings. Both words refer to distance, but the distinction is in the type of distance. Further refers to mental distance, while farther refers to physical distance. Take a look at the differences as illustrated in the sentences below:
Example 1 (further-correct usage): The student read further in the textbook. (Note that the distance traveled is only mental.)
Example 2 (farther-correct usage): I have to drive farther to work than to school. (In this sentence, we are referring to an actual distance that is measurable in miles, kilometers, etc., so the word farther is used.)
The same distinction holds true when used as an adjective.
“I live in the farther city.”
“Nothing could be further from the truth.”
As far as I know, only further can be used as a verb.
You can “further your education”, but you can’t “farther your trash from the house to the curb”.