A great choice as well, and of course Mel Gibson has his problems but have him or Sigourney Weaver ever looked lovelier?
Featured at the end of the film Master & Commander is Boccherini’s Musica nocturna de las calles de Madrid
Starts at 50 seconds here:
Master and Commander. End Titles. Boccherini - YouTube
A slightly better rendition, in my opinion, can be found here. The part featured in the movie starts at 4:15
Boccherini- (Master and Commander) - YouTube
Regardless of the missteps he may have taken, I will always be a Mel Gibson fan. He won me over long ago with Gallipoli and The Road Warrior.
Ah! superb, one of my favourite films and certainly one of the great ending themes
Why yes…yes he has…
As a young man he was certainly very easy on the eye.
And it appears we have stumbled into period of Peter Weir appreciation, no bad place to be in my opinion.
Some other memorable themes:
Luscious Sandra Dee, mmmmmmmmmmm! 
though I always associate this tune with the movie:
Similarly, this is not the main theme to Zorba the Greek, but it’s so inextricably linked with the film I’m posting it anyway:
And we’re back to Omega Man (RE: A Summer Place)
Speaking of the luscious Sandra Dee
Since your clip is “age restricted,” I’ll supplement it with this one for those who can’t or don’t want to log in to YouTube:
That track fits the video better anyway.
This same song was used to brilliant effect in the British comedy Lock, Stock & Two Smoking Barrels
lock stock and two smoking barrels “Zorba’s Dance” - YouTube
The Bounty theme reminds me of this one, first heard in Star Trek: The Motion Picture:
(I’m not posting the main theme to that movie because it was used later for the TV series ST: TNG.)
I posted in the Picard thread my objection to using over and over the Goldsmith motif for Worf when Ron Jones did his own Klingon motif for TNG.
Yes I know Goldsmith >>>>> Jones, but…
The theme from Breaker Morant:
“In the Heat of the Night” written by Quincy Jones, performed by Ray Charles.
“The Third Man Theme” written and performed by Anton Karras. It was written years before the film, but never previously recorded or released.
This brings back some good memories. I wish I could go back to the '80s… 
I love all Bacharach…even this:
