Real successor of Mstislav Rostropovitch, Alexander Kniazev studied the cello at the Moscow Conservatory under Alexander Fedorchenko and learned to play the organ under the famous Miss G. Kozlova. 
He won the International Cello Competition of G. Cassado, the International Chamber Music Competition of Trapani and the International Competition of Pretoria (UNISA) in South Africa.

Alexander Kniazev played under  famous conductors like: E. Svetlanov, Y. Temirkanov, M. Rostropovitch, Y. Bashmet, V. Fedoseyev, M. Shostakovitch, N. Järvi and K. Mazur. He  performed with the Royal Philharmonic of London, the Bavarian Radio Orchestra, the Göteborg Symphonic, The Den Haag Residentie Orchestra, the Orchestre National de France and the Prague Philharmonic.
He was also invited at the Moscow festival “Les soirées de Décembre”, which was organised by S. Richter, who significantly influenced him.
Among his partners in chamber music can be mentioned Brigitte Engerer, Evgeny Kissin, Vadim Repin, Plamena Mangova, Boris Berezovsky, Dmitri Makhtin and Nikolaï Lugansky.
Alexander Kniazev also performed as a trio with Boris Berezovsky and Dmitri Makhtin on the prestigious scenes of the Concertgebouw (Amsterdam), at Brussels Palace of Fine Arts, at  London Wigmore Hall, at  Salzburg Festival, and will soon perform at the Lincoln Center of New York. He played in many prestigious hall  like Musikverein of Vienna (with Vladimir Fedoseyev), La Salle Pleyel of Paris (Dvoràk concerto); he has been invited at the Montpellier Festival in July 2009 with Evgeny Kissin and Silvia Marcovici. In 2010, Alexander Kniazev peformed Bach Six Suites at the Philharmonia of St Petersbourg.
The Trio recorded a DVD dedicated to Tchaïkovsky with the pieces for piano, violin and cello, and the Trio Elégiaque « A la mémoire d’un grand artiste ». This DVD was awarded the « Diapason d’or ».

His Ernest Bloch CD, « Schelomo », which was recorded with the Russian State Symphonic Orchestra and E. Svetlanov conducting, was highly acclaimed by the International musical press. Furthermore, his « Max Reger » CD was chosen amongst the best by the French music magazine « Répertoire ».
Recordings with Warner Classics International include a CD dedicated to Bach Cello Suites; Shostakovitch Trio n°2 and the Rachmaninov Trio Elégiaque with Boris Berezovsky and Dmitri Makhtin, has been awarded the « Gramophone prize », the « Diapason d’Or » and the « Echo Award».
The same label, released a Tchaïkovsky album with the Chamber Orchestra of Moscow and Constantin Orbelian including the Variations Rococo, Andante Cantabile and Romances, and the two Mendelssohn trios with Dmitri Makhtin and Boris Berezovsky  which were awarded the « Echo Award».
Warner Classics International released the Dvorak cello concerto with the Tchaïkovsky Symphony Orchestra of Moscow, and Vladimir Fedoseyev; Alexander Kniazev went on an European tour with the same programme.