Books
Books: Biographies, Criticism, Analyses
Rush, Brian Harrigan (Cherry Lane Music: 1984)
Success Under Pressure, Steve Gett (Cherry Lane Books: 1984)
Visions, Bill Banasiewicz (Omnibus Press: 1988)
Mystic Rhythms, Carol Selby Price and Robert M. Price (Wildside Press: 1999)
Merely Players, Robert Telleria (Quarry Music Books: 2002)
A Simple Kind Mirror, Leonard Roberto, Jr. (iUniverse (vanity press), 2002)
Contents Under Pressure, Martin Popoff (ECW Press: 2004)
Chemistry, Jon Collins (Helter Skelter Publishing: 2005)
Rush, Rock Music, and the Middle Class, Chris McDonald (Indiana University Press: 2009)
Rush and Philosophy, Jim Burti and Durrell Bowman, editors (Open Court: 2011)
Rush: The Illustrated History, Martin Popoff (Voyageur: 2013)
Rush FAQ, Max Mobley (Backbeat: 2014)
Rush: Life, Liberty, and the Pursuit of Excellence, Robert Freedman (Algora: 2014)
Experiencing Rush, Durrell Bowman (Rowman & Littlefield, 2014)
Rush -- Chronology (Patrick Lemieux Across The Board Books 2015)
Rush -- Album By Album (Voyageur Press: 2017)
Books: Neil Peart
The Masked Rider, ECW Press: 1996
Ghost Rider, ECW Press: 2002
Traveling Music, ECW Press: 2004
Roadshow, ECW Press: 2007
Far and Away, ECW Press: 2011
Far and Near ECW Press 2016
Far and Wide ECW Press 2018
Additionally, there is The Art Of Rush (Hugh Syme) and Wandering The Face Of The Earth.
It really depends on what aspect of the band you want to know about. There's your straight bio's that cover up to the book's publication, songs interpretations, construction of the music, lyrical and music criticism, philosophy, inspirational stories, reference material.
Don't have the Rush FAQ Book or the most recent Popoff but still have the rest.
If I were to do a top 5 in no order (discounting the Neil books which are their own different thing.) it would probably look like this.
Chemistry
Wandering The Face Of The Earth.
Rush -- Life, Liberty and the Pursuit of Excellence
Chronology
Rush, Rock Music and The Middle Class
Experiencing Rush
Well, OK that's 6.