During this phase you can build new ships for your fleet.  You can build ships only in sectors containing a world owned by you (or one of your allies), and the requisite number of RU must be present at that world.  If you (or your ally) lose ownership of a world before this phase, or if you fail to stockpile the necessary RUs, the build instruction will be cancelled.  You cannot build ships on a world during the same turn that you take control of it, nor can you build on a world that is interdicted.

Unique serial numbers are assigned automatically to each ship built.  You may give a name to each ship you build, although those names must be unique for each ship in your empire.   Ship names can be any combination of alphanumeric characters, but they must contain at least one non-numeric character.
 
Allies: Allied empires may build new ships at worlds owned by their allies, assuming they have created a sufficient RU stockpile of their own at the foreign world.  See the Transfer Resource Units phase.  If you build a ship on an allied world, that ally automatically acquires that ship's design (i.e., it's impossible to hide the details of a ship's construction at a world owned by someone else).
 
Abandoned Empires: Abandoned empires always build on any world where there are stockpiled RUs.  New ships to be built will alternate between the class which has the most DP that can be afforded and the most guns that can be afforded (choosing the cheapest design in the case of ties), until no RUs are left with which to build.