Only one carrier of any class in their navy, and that's arguably unoperational.
Among other things, the Russians have still to check on who owns exactly what as far as the Crimea and the Black Sea are concerned: Russia or the
new Ukraine: so responsibilities for port facilities are often in doubt.
The Kuznetsov's sister-ship: was the Tbilisi (then Georgia went) and became Admiral Gorshkov, was at the heart of a long and sorry saga of
negotiating a sale with India (you'll find that searching the ship's name).
The interest in the Soviet avaition cruiser programme is that it is a very clear-cut and neat example of how the Soviets' attempts to match the USA
as a super-power led inevitably to bankruptcy: what must have been wasted on this line of aborted progammes beggars belief.