River is the Child of the TARDIS, having been conceived while in flight in the time vortex.
In Doctor Who(2005-) Season 6 Episode 8 "Let's Kill Hitler" at 40:10 River states "I seem to be able to fly her, she showed me how, she taught me. The Doctor says, I'm the Child of the TARDIS."
Then in Doctor Who (2005-) Season 5 Episode 12 - "The Pandorica Opens" , at 40:00 the Doctor says to River "You're flying it wrong" River responds with "I'm flying it perfectly, you taught me".
So River was taught by both the Doctor, and the TARDIS.