In which landmark case did the Supreme Court establish the doctrine of "separate but equal"?

The landmark case that established the doctrine of "separate but equal" is Plessy v. Ferguson. In this 1896 decision, the Supreme Court ruled that racial segregation laws did not violate the Equal Protection Clause of the Fourteenth Amendment as long as the segregated facilities for the different races were equal in quality. The case arose from a challenge to Louisiana's segregation laws, where Homer Plessy, a man of mixed racial heritage, was arrested for sitting in a "whites-only" car of a train. This ruling legitimized racial segregation for decades and provided a legal foundation for the continuation of discriminatory practices in various aspects of public life. The doctrine of "separate but equal" was not successfully challenged until the mid-20th century, particularly in the famous case of Brown v. Board of Education, which ruled that racial segregation in public schools was inherently unequal and unconstitutional.