How they put heavy cranes on top of the building?

Question

I saw crane on very tall building. How do they put such heavy item on such high building?

Answer 1

Quite simple, lift it up there with another crane that is more expensive once it's up there the expensive crane is sent away and they can use the "cheap" crane for construction.

Afterwards the expensive crane returns to get the construction crane down.

but most of the times they are from the ground up and attached to the building (see image)

The crane can lift itself higher when required (see video in link)video

Answer 2

They lift it up in pieces and assemble the crane in place using a second mobile crane they bring in to build it.

The heaviest parts will be the winch assembly and the counter weights.