They claim it's the oldest underground urban transportation system. In fact, they claim that Paris not only stole the idea from them, but the name as well — London's rail system was first called the Metropolitan, but that was before it went underground, which happened in 1890.
Only about half of the Underground is actually underground.
Today it's an extensive system of tracks and cars, above and below ground, that travels to the far outskirts of London. Used largely by commuters, the Tube, as the Underground is usually called, also makes it easy for visitors to get around. It's easy to use, affordable, and a map is all you need. Plus some tickets!
Maps come and maps go, but the Tube is forever, so it seems. The early maps were pretty much a representation of the of the actual geographic routes and could easily be superimposed on a street map of London.
It wasn't until the 1930s that an engineer working for the Underground had the thought that riders on the trains didn't really care what was above them, they just wanted to know what station was next, and how the connected. So, Harry Beck created a schematic map, inspired by electrical wiring diagrams.
You're probably comfortable reading the Beck map, since it's what inspired most of the subway systems maps around the world today. Back in 1933, though, it was an immediate hit and his map was eventually replaced until he was "rehabilitated" after his death. The modern London Tube maps are once again based on Beck's work.
Here's what the current London Tube map looks like. It's clear that it's a descendant of the Beck Map. That is, it's a schematic representation of the system. It's not a map that matches a street map. Look at the shape of the Thames River on the map to get an idea of just how graphical it is.
This size is a little hard to read, so here's a link to the full-size map, complete with an index of all the stations.
As we said, Beck's 1933 map has been an inspiration to the graphic artists who design other maps. Some of us, though, may be more comfortable with a map that is more geographically accurate.
It seems that there's a "remix" culture playing with the London Tube map, giving it a different spin, or tugging it back in shape to match the streets above. The map above is a an excerpt from a more geographic version of the map, remixed by Sameboat at Wikimedia Commons.