Is "Collusion" Illegal?

I read that lefty Jimmy Fallon ridiculed Rudy Giuliani for saying that "collusion is not a crime."  Fallon was incredulous, or feigning so, claiming that Trump must be thinking "why can't this guy just shut up?'

The meaning of collusion is "a secret agreement or cooperation."

Well is collusion illegal?  Not according to attorney Gregg Jarrett.  Writing in his recently released book "The Russian Hoax," Jarrett writes:

"Collusion" is not a crime, except in anti-trust law. Reporters and anchors never bothered to cite a specific statute because none could be found in the criminal codes.  Not that they ever bothered to look.  They were satisfied, indeed anxious, to level the accusation because their bias against Trump was so impassioned and pervasive that it became impervious to the facts.

I am reading Jarrett's book now.  It recounts the crimes of Hillary and the steps to improperly exonerate her in detail, naming names, dates and places.  I recommend this book.

Note:  Collusion itself isn't illegal, but leads to illegality when its object is to commit a crime.  If you collude with your neighbor to throw a surprise party for your wife, that isn't illegal.  If Democrat media colludes with others to launch an "October surprise" in order to damage a Republican candidate's chance for election, that too is not a crime (dirty pool, maybe).

No description of any collusion of Trump with Russian agents to somehow skewer Hillary's chances has ever been made or alleged.  No description of any crime such collusion entailed has ever been made. So what exactly is Mueller investigating?