The following are the facilities that can be built in the Avenger. Unlike the first game, XCOM 2's base is now mobile. The Avenger is an alien ship that was taken over by the XCOM survivors. The HQ in the first game is an underground base that the player chooses where to place in the world right in the beginning of the game. Hence, there are lot more rooms available in XCOM: Enemy Unknown / Enemy Within than in this incarnation.
Default Buildings (non-buildable, cannot be demolished, and unupgradeable),
Armory
Commander’s Quarter
Engineering
Living Quarters
Research
Facilities
Advanced Warfare Center
Guerilla Tactics School
Proving Ground
*Order is alphabetically, not an actual build order.