Thanks for the ITA help. I was able to find the following itinerary that I'd like to book; however, how do I actually book this since it's partially British Airways, AA and Finnair? And seems to be much more expensive to book through any single one of those carriers.

Austin (AUS) to Dallas/Fort Worth (DFW) - Fri, Dec 20
British Airways p.l.c. 1842 Dep: 2:20PM Arr: 3:25PM
OPERATED BY AMERICAN AIRLINES INC.

British Airways p.l.c. Dallas/Fort Worth (DFW) to London (LHR)
British Airways p.l.c. 192 Dep: 4:45PM Arr: 7:25AM Economy (H)

British Airways p.l.c. London (LHR) to Berlin (TXL) - Sat, Dec 21
British Airways p.l.c. 992 Dep: 8:35AM Arr: 11:25AM Economy (H)


Finnair Oyj London (LHR) to Dallas/Fort Worth (DFW) - Sun, Jan 5
Finnair Oyj 5793 Dep: 12:05PM Arr: 4:30PM Economy (N)
OPERATED BY AMERICAN AIRLINES INC.

American Airlines Inc. Dallas/Fort Worth (DFW) to Austin (AUS)
American Airlines Inc. 2482 Dep: 6:30PM Arr: 7:30PM Economy (N)

Cost per passenger (including taxes & fees) $1,739.30