The early maps for the London Underground were all based on geographical maps, and so the central stations were bunched tightly together while only the farther, suburban stations could be easily seen, with space between them. By the end of the 19th century there were maps for individual lines but there wasn't a complete map that showed all the possibilities for travelling through the city.
This improved in 1907 when a newspaper called 'The Evening News' published a small map called 'The Evening News London Tube Map'. It showed all of the various underground lines and was also the first map that used different colours for each of the lines – there were eight of them at this time – making it easier to distinguish them.
The map was still geographical, and only extended, as did most of the Underground lines at this time, partway into the suburbs and was thus contained. Over the next few decades Tube lines reached out towards Uxbridge, Hounslow and Barking making it impossible to make a compact geographical map.
A London Underground employee named Harry Beck was the first to notice that the Underground was, in fact, mostly underground, and thus there was really no need to show people the landmarks that it zoomed underneath. All that was needed was a diagram to show the sequence of the stations, and the points of transfer.
In 1931 Beck designed the first diagram that depicted all of the stations, lines and transfers in a neat, concise form. It resembled electrical circuit diagrams although Beck insisted that these were not the source of his idea. He wasn't commissioned to design his map, and the authorities of the Tube were skeptical about it, but he persisted. Eventually they released a small number of copies of his map as a trial. The rest, as they say, is history. The public snapped them up and the geographical maps soon became, well, history.
The diagrammatic London Tube map has been revised and improved many times since the early 1930s when it first appeared, with new lines added and other refinements such as indications of overground train transfers. The enthusiasm of Harry Beck led to this innovation, and now every major city in the world has spread his breakthrough into other lands and cultures with their own underground transport maps.