The Red Room was a Soviet program designed to train young women as infiltrators and assassins. It fell under the program known as Otdeleniye Nulevoy, the Russian equivalent to the US Program Weapon Plus.
Graduates of the Red Room were most frequently trained as ballerinas. It gave an excellent cover for international travel, explained their extreme fitness, and made them unlikely suspects. They were instructed in covert tradecraft, assassination, marksmanship, hand-to-hand combat, and foreign languages.
The head of the Red Room since inception has been Lyudmila Kudrin, aka 'Mother'. She created the Widow protocols and used her trainees as test subjects for the Infinity Formula. She herself was not an ideal match for the Infinity Formula and has been heavily augmented by experimental cybernetics.
Many Red Room assets were lost when the Soviet Union collapsed. A faction of Soviet Restorationists called Katyusha were able to recruit Lyudmila and her girls. The program goals were expanded to train the girls to steal valuable technology and research. The 'Science Class' was developed for girls with the proven aptitude for science who were otherwise not deemed capable of graduating from the standard Red Room curriculum.