Alva J. McClain’s The Greatness of the Kingdom argues that 
* “the Kingdom of God” is the grand central theme running through all of Scripture. 
* He treats it as a single divine kingship with rich, 
* sometimes paradoxical features that Scripture reveals across the Old and New Testaments, and 
* he builds his case through an inductive, passage-by-passage study of biblical material.

A key framework in the book is that the kingdom involves 
* (1) a ruler (God), 
* (2) a realm (the domain over which he rules), and 
* (3) the exercise of rule (how the reign is carried out). 

McClain distinguishes two aspects (or phases) of one reign:

* a universal aspect—reflecting the extent of God’s rule over all creation, and 
* a mediatorial aspect—reflecting the method of rule, where God governs through a mediator who acts as the representative king.

From there, McClain emphasizes the mediatorial kingdom as 
* being tied to redemption, beginning with God’s covenantal dealings in Scripture (including a climactic establishment associated with Sinai), and 
* moving forward through prophets and the life and teaching of Jesus. 

He argues that the kingdom is presented as “at hand” when the King is present, but that Israel’s rejection and God’s unfolding plan shape how the kingdom’s history develops. In his view, 

* the kingdom offer continues through the Acts period while the church takes root, and 
* later the mediatorial kingdom reaches fulfillment in the millennium, after which 
* Christ’s reign transitions in the final consummation of God’s purposes.

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mediator /me'de-a"t?r/
noun
One that mediates, especially one that reconciles differences between disputants.
A substance or structure that mediates a specific response in a bodily tissue.
A subatomic particle that effects or conveys a force between subatomic particles.
One who mediates; especially, one who interposes between parties at variance for the purpose of reconciling them; hence, an intercessor.
One who negotiates between parties seeking mutual agreement.
A negotiator who acts as a link between parties.
The American Heritage® Dictionary of the English Language, 5th Edition • More at Wordnik