The Smolny Institute for Young Ladies of Noble Birth was founded by Catherine the Great in 1764 in an effort to provide trained musicians and performers for Court entertainments who were not "actresses". Â The girls of the Institute were described by Nelidov as "the vestal virgins of Russian Culture, worshipping the Goddess Catherine" Â
Levitsky painted six potraits of the Institute's top pupils in the 1770's which depict them acting in plays, dancing, and performing. Â They now grace the Russian Museum, and depict:
Feodosiya Stepanovna Rzhevskaya (on the right) (1760-1795)- daughter of general-lieutenant Stepan Matveevich Rzhevsky and Sofia Nikolayevna, née Baroness Stroganova. Finished the Smolny Institute for Young Ladies with honors. Married Prince M. N. Golytsin, State Councillor, later the Governor of Yaroslavl province.
Princess Nastassiya Mikhailovna Davydova (1764 - ?), daughter of general major Price Mikhail Mikhailovich Davydov, the Governor of Tambov province in 1780s.
Nelidova, Ekaterina Ivanovna (1758-1839) - daughter of lieutenant Ivan Dmitrievich Nelidov. She was raised in the Smolny Institute for Young Ladies and was noticed there by Empress Catherine II, who made her a maid of honor to the Grand Duchess Maria Feodorovna, later Empress, whose husband Emperor Pavel I was charmed by the grace and vivacity of Nelidova, and she was sincerely attached to him, although their relations were never intimate. She was able to influence Pavel I, prevent his unwise decisions and tantrums. She was also a close friend of the Empress Maria Feodorovna.
Khruschova, Ekaterina Nikolayevna (1761-1811), daughter of prime-major Nikolay Semenovich Khruschov and Praskovya Mikhailovna, née Volkonskaya. In 1767-1779, studied in the Smolny Institute, which she finished with honors. Her success in studies was noted by Catherine II and the King of Sweden Gustav III, who presented the girl with jewelry inlaid with diamonds.
Khovanskaya, Ekaterina Nikolayevna (1762-1813), princess, daughter of colonel, Prince Nikolay Vasilyevich Khovansky and Maria Nikolayevna, née Schepotyeva. In 1767-1779, studied in Smolny Institute, which finished with honors. In 1786, married Yuri Alexandrovich Neledinsky-Meletsky, poet, Secretary of State of Emperor Pavel I, senator. In 1798, moved with her husband to Moscow. Died in 1813, in Yaroslavl, where the family had escaped from Moscow, occupied by the French army of Napoleon in 1812.
Levshina, Alexandra Petrovna (1757-1782), daughter of prime-major Peter Ivanovich Levshin and Tatyana Ivanovna, née Princess Koltsova-Masalskaya. In 1764-1776 studied in Smolny Institute which finished with major gold medal. In 1778 was appointed a maid of honor to Catherine II. In 1780 married the captain of Izmailovky regiment Prince P.A. Tcherkassky. Died in Moscow and buried in Donskoy monastery.
Borschova, Natalya Semenovna (1758-1843)- daughter of Semen Ivanovich Borschov. In 1764-1776 studied in Smolny Institute, which finished with major gold medal, was very good in singing. In 1776 was appointed a maid of honor to Grand Duchess Maria Feodorovna. In 1809 was appointed the Head (hofmeisteress) of all the maids of honor of Emperor court. She was awarded the Order of St. Catherine. Was married twice, her first husband K. S. Musin-Pushkin, after his death married general-major Baron von der Hoven. Died in St. Petersburg and buried on Smolensk cemetery.
Molchanova, Ekatherina Ivanovna (1758-1809), daughter of collegiate councillor Ivan Yakovlevich Molchanov. In 1764-1776 studied in Smolny Institute, which finished with major gold medal. In 1776, was appointed a maid of honor to Grand Duchess Maria Feodorovna, then to Catherine II. In 1780, married S. A. Olsufyev, later general-major.
Alymova, Glafira Ivanovna (1758-1826) - daughter of colonel Ivan Akinfievich Alymov. Studied in Smolny Institute, finished it with gold medal; was one of the best harp players of her time. Since 1776, a maid of honor to Catherine II, later lady-in-waiting. Her first husband was A. A. Rzhevsky, author, freemason, vice director of the Academy of Science. Her second husband was I. P. Maskle, translator, later consul of Russia in Nice. She was awarded the Order of St. Catherine. Buried in Vagankovsky cemetery in Moscow.
Vorontsova, Ekaterina Alekseyevna (? - 1784) daughter of Admiral Aleksey Naumovich Senyavin. Maid of honor to Catherine II. Married Count S. R. Vorontsov, ambassador of Russia in Venice. Had two children: son M. S. Vorontsov, later prince and govenor-general in the Caucasus, and daughter E. S. Vorontsova, later Lady Pembroke. She died in Italy, buried in Venice in Greek Church of St. George.
I do not believe the girls recieved much practical education at the beginning, but I do know that by the end, the pupils were also offered Russian History and literature, Modern Languages, basic Sciences and Math  along with their extensive cultural training.
After the Revolution, the Institute became the headquarters of the Revolutionary Government. Â Here is an interesting description of the Institute after the revolution.
http://216.239.41.104/search?q=cache:rofgN9XN_AYJ:digital.library.upenn.edu/women/bryant/russia/russia-IV.html+Smolny+Institute+for+Young+Ladies&hl=en&ie=UTF-8Best,
Nick