When I wrote regularly about the Tube, I received a letter from an Austrian who said he was fascinated by two things about London: the way houses had their gutters and drainpipes on the outside, and the smell of the Underground, which he thought so evocative it should be bottled and sold. On another occasion, I had dinner in Paris with a man who conducts historical tours of the Metro. He told me that the Metro bosses he knew were in awe of the people who ran London's Tube because doing so must be "the most incredible challenge".

The Metro was built according to fairly consistent principles over little more than 30 years. The lines are not far below ground, and they are straight, with few complicating spurs and branches. Trains can therefore be shuttled back and forth along them at frequent intervals. The Underground, by contrast, is an agglomeration of lines built over a long period by dysfunctional top-hatted men pursuing their own zany visions. It is the most eccentric and ramshackle system in the world, but also the most interesting.

I could pick the Northern Line as the craziest in conception and the most unworkable. Essentially an ill-advised melange of the City & South London Railway (started in 1890) and the Charing Cross & Hampstead Railway (begun 1907), the Northern Line's City and West End branches should logically be unpicked and separated. Meanwhile, they converge in fearful knots at Euston and Camden.

The line with the oddest shape of all is the Circle, the strangeness of which begins with the fact that it does not actually exist. The only bits of track that properly belong to it run between Gloucester Road and High Street Kensington and between Tower Hill and Aldgate. These were reluctantly built in the 1880s, under pressure from government, by the Metropolitan Railway and the Metropolitan & District Railway as a means of creating a circle out of their two separate lines. Well, it seemed a good idea at the time. But by 1914, it was being noted that only 20 per cent of its passengers went around the "corners" of the Circle. And nobody ever goes all the way round. Try buying a ticket to King's Cross at King's Cross and the machine practically explodes with indignation.

In an attempt to provide a smooth service, trains begin approaching the Circle from various directions at 5am, but the line is constantly prey to problems on the Met, the District and the Hammersmith & City, all of whose tracks it uses. The result is the lowest peak-hour frequency of any line, with trains arriving - if at all - approximately every eight minutes. But don't blame the signal controllers or the drivers or the managers. Blame history.

Consider also the westerly complications of the District Line, which basically goes mad left of Earl's Court. The various destinations of the trains arriving at Earl's Court are shown by an illuminated arrow appearing next to the words "Richmond", "Wimbledon", or whatever, on indicator boards that are getting on for a hundred years old and are Grade II listed so cannot be removed. Unlike modern boards, they show only the destination of the next train, not the one after that. So watching them is like playing roulette, and similarly bad for the heart. Then again, they are very beautiful.

The Underground is littered with such historical anomalies. Look at the southbound Northern Line platform at Warren Street: elegant, bold tiles proclaim "EUSTON ROAD", which the station hasn't been called since 1908. Equally attractive tiles proudly spell out "GILLESPIE ROAD" at the Piccadilly Line station which stopped being called that in 1932, when it became Arsenal. Any commuter who developed an interest in Underground tiles, incidentally, would have a hobby for life, and a constant distraction from the pain of delays and cancellations. Look at the gorgeous, one-off colour schemes of Covent Garden (yellow, white and orange) and Russell Square (cream, green and red), created by the Edwardian design genius Leslie Green, possibly so that the illiterate could recognise their home stations.

Some of the Underground's historical mistakes can be enjoyed from the streets. Almost every day I cycle past a Cash Converter shop that used to be Kentish Town South station. This has an undistinguished history, having been opened in 1907 and closed in 1924. It was simply too close to Kentish Town station. John Betjeman, who wrote a short story about a man who accidentally gets off at Kentish Town South and is trapped in the closed station, said it was like "a comma unwontedly interposed into a sentence". Every so often, a man from the Underground goes into the Cash Converter and disappears through a trap door to check the abandoned station for rats.

Ever eaten at Pizza on the Park in Knightsbridge? That was Hyde Park Corner station until 1932, when the installation of escalators required a new station to be constructed over the road. After lunch there, stroll over to stately, stucco-fronted Leinster Gardens in Bayswater, and look hard at numbers 23 and 24. Something a little fishy here? Well, the windows are painted on for a start, and these "houses" are only about 5ft thick, the structure being nothing more than a cosmetic screen. It was created in the late 1860s to conceal a cutting of the Metropolitan and Metropolitan & District lines where the customised steam trains then used on the Underground would release the balls of smoke they'd been storing up.

The aim of the project was to preserve the decorum of Leinster Gardens, and it is deference to property holders that explains the numerous "gaps" on the Underground. These occur, between relatively inflexible train and curved platform, whenever a line has to squirm to avoid going under an important set of foundations: as at Bank, where it was necessary to avoid the Bank of England. The Underground gamely dealt with this by installing, in 1969, one of the world's first digitally recorded announcements: "Mind the gap."

My point is twofold. Think of those who operate the Tube not as incompetent buffoons, but as martyrs to history; and savour, in an increasingly bland and ahistorical world, the perplexities with which they must grapple.