put together

1.  Build, assemble, create, as in We put together the new bookcase, or This writer can't put together a coherent sentence. [First half of 1500s]
2.  Combine mentally, as in Once she put this and that together she knew exactly what had happened. [First half of 1600s] Also see put our heads together; put two and two together.

The verb has one meaning:

Meaning #1: make by putting pieces together
  Synonyms: assemble, piece, set up, tack, tack together

The adverb put together has one meaning:

Meaning #1: in conjunction with; combined
  Synonyms: jointly, collectively, conjointly, together