Not only does the American Ballet Theatre arrive at the Kennedy Center Tuesday, but a major, sumptuously produced work on the ABT is also being published this week. Written by Charles Payne, long associated with the company, the copiously illustrated work chronicles the history of the company from its tentative beginnings in 1939 as the Ballet Theatre ("American" was added in 1957) to its present rank as one of the finest ballet companies in the world.

With an insider's yee, Payne details the development of this unusual company - its sources of inspiration, its directors, benefactors, choreographers, dancers, productions, tours, and economic vicissitudes. And with choreographers as diverse as Fokine and Twyla Tharp and dancers of the stature of Markova, Alonso, Kriza, Bruhn, Kirkland, and Baryshnikov - to name just a few - Payne is never dull. His grasp of facts (based largely on experience and refreshed by access to extensive archives), his sharp observations and anecdotes make the reader feel part of the company's negotiations and backstage drama.

The illustrations can take equal billing. With over 500 photographs in black and white and color by Cecil Beaton, Richard Avedon, Martha Swope and others, virtually every ABT production (grouped by decade with an overall commentary by Payne) is illustrated - many productions with five or more photographs each. There are also individual portraits of principal dancers, as well as informal shots of the company practicing and relaxing.

Rounding out this impressive work are three essays by dancers associated with the company: Nora Kaye on "The Lure of Ballet Theatre," Erik Bruhn on "Restaging the Classics," and Alicia Alonso on "Performing Giselle. " These are followed by another essay, "Directing a Ballet Company," by Lucia Chase, founder, benefactor, co-director and former dancer of the ABT. Finally, there is a complete listing of ABT productions from 1943 to 1977, detailing choreographer, music, scenery and costumes, dates of company and world premieres, principal dancers or cast. (Knopf, $35)