What is the name of the rapid transit system serving Seoul, South Korea?

The rapid transit system serving Seoul, South Korea, is called the Seoul Metropolitan Subway.

It is a large metropolitan railway network rather than a single operator-owned subway. The system combines Seoul Metro routes, Korail commuter and regional services, Incheon Metro lines, and several light-rail or people-mover lines serving Seoul, Incheon and surrounding Gyeonggi Province. That broad structure is why the name refers to the metropolitan area rather than only Seoul city.

Construction of the first subway line began in 1971, and Line 1 opened in 1974. Seoul Metro’s numbered Lines 1 through 9 form the best-known core, but the wider system also includes through-running national railway services and separately operated lines.

Korail is therefore not the answer to the question: it is one of the major operators within the network. Busan Metro and Daegu Metro are separate urban systems serving other South Korean cities. The Seoul Metropolitan Subway is also commonly called the Seoul subway in everyday English, but the longer name is the canonical system name.