how a tower crane for a high rise building construction is erected?
Depends on the type - if the building is not that tall, the tower crane could be built by any taller crane (either a mobile one or an existing one on the site). If the building is very tall, a self-erecting crane is usually used; this type has a sort of jack mechanism somewhere in the tower (usually near the bottom), so as it is needed, the existing tower can be lifted, and another tower section is inserted to raise the entire structure, repeating the process as needed as the structure the crane is building gets taller (thus, the crane is building itself as it goes along).