https://en.wikipedia.org/wiki/Transit_map#History

The mapping of transit systems was at first generally geographically accurate, but abstract route-maps of individual lines (usually displayed inside the carriages) can be traced back as early as 1908 (London's District line), and certainly there are examples from European and American railroad cartography as early as the 1890s where geographical features have been removed and the routes of lines have been artificially straightened out. But it was George Dow of the London and North Eastern Railway who was the first to launch a diagrammatic representation of an entire rail transport network (in 1929); his work is seen by historians of the subject as being part of the inspiration for Harry Beck when he launched his iconic London Underground map in 1933.

After this pioneering work, many transit authorities worldwide imitated the diagrammatic look for their own networks, some while continuing to also publish hybrid versions that were geographically accurate.