The Alvin Ailey American Dance Theater, which begins a week of performances at the Kennedy Center Opera House tonight, arrives with the most varied and novel programs the troupe has brought to Washington in years. Thursday evening's fare will include a world premiere of an untitled work by Jennifer Muller. Among the total of 13 dance works to be offered, six others will be area premieres. Besides Muller and Ailey himself, the choreographers include George Faison, Donal McKayle, Rudy Perez, Louis Falco and John Butler. Of special note: McKayle's "Blood Memories," a 50-minute work tracing the history of black peoples from the Nile to Harlem: and Ailey's "Three Black Kings," set to the late Duke Ellington's last completed score. The company will present a free lecture-demonstration at noon Wednesday in the Kennedy Center Concert Hall.

With the help of grants from the D.C. Commission on the Arts and Humanities, the Queene Ferry Coonley Foundation and other donors, the Dance Project is offering 10 modern dance scholarships for a 25-week program in dance, arts management and theater techniques. Auditions, open to dancers 16 and over, will be held Saturday in the Dance Project studio at 2424 18th St. NW (entrance in rear) at 1:45 p.m. for intermediate levels and 2:45 for elementary levels. For information, call 462-1321.

The Bolshoi School of Ballet, directed by Yuri Vzorov, announces full scholarships for male dancers for the school's complete Vaganova curriculum. For details, call 652-3336 weekdays between noon and 3 p.m.

A new ballet company, Potomac Ballet Theater, is rehearsing weekly in a converted barn in western Fairfax County for debut performances in May. Directed by Richard Brown, former director of the National Ballet's school, the youthful troupe has recruited some dozen dancers who have studied with such teachers as Robert Joffrey, Edward Villella, Arthur Mitchell, Alvin Ailey and Leon Fokine. Brown, who also teaches ballet at Western High School, has been the artistic director of such other companies as the Norwegian State Ballet, the National Ballet of Iran and the Glasgow Theater Ballet.

A comprehensive exhibition of the work of Russian painter Leon Bakst, one of Serge Diaghilev's most inspired collaborators, is on view this month at Davis and Long, 746 Madison Ave., New York City. The show, which drew 11,000 viewers in Edinburgh and large crowds in London, includes Bakst's designs for ballet and theater, fabrics, portraits, nudes and landscapes.