ldquo;Sleeping Beauty rdquo; rsquo;s rich, magical story, known by all, illustrates both the struggle between good and evil and the evolution of a girl. We see Princess Aurora grow from the confident and delicate adolescent of the famous ldquo;Rose Adagio, rdquo; in Act I, into a woman in love by the end. In the ballet rsquo;s second and final week at City Ballet, the transformation will be undertaken mdash;for the first time mdash;by the up-and-comers Sterling Hyltin and Megan Fairchild, as well as by Wendy Whelan and the infinitely self-possessed Ashley Bouder.
Next week, the company presents the first of its mixed bills, with a selection of Balanchine rsquo;s Stravinsky ballets. 
Jan.
10 at 7:30, Jan. 11-12 at 8, Jan. 13 at 2 and 8, and Jan.
14 at 3: ldquo;The Sleeping Beauty. rdquo; Jan.
16 at 7:30: ldquo;Agon, rdquo; ldquo;Monumentum pro Gesualdo, rdquo; ldquo;Movements for Piano and Orchestra, rdquo; ldquo;Duo Concertant, rdquo; and ldquo;Symphony in Three Movements. rdquo; (New York State Theatre, Lincoln Center. 212-870-5570.
Through Feb. 25.)
The events of the final week of the festival, which is anchored by a series of programs at the Walter Reade Theatre, include a presentation of the filmed version of Mark Morris rsquo;s opera-ballet ldquo;Dido and Aeneas rdquo; and a screening of Gene Kelly rsquo;s grand experiment ldquo;Invitation to the Dance, rdquo; from 1956.
Kelly, working in his more classical vein, meant to create a film for the general public entirely out of dance, pantomime, and animation. He used famous ballet dancers of the time and pranced around with animated characters; the studio was perplexed, and the movie fizzled. The screening of ldquo;Dido rdquo; is followed by a discussion with Morris and the director of the film, Barbara Willis Sweete, moderated by Joan Acocella.
(Lincoln Center and other locations. 212-875-5600. Jan.
13 at 2 and 4. For a complete schedule, visit www.dancefilmsassn.
org.)
The Japanese troupe brings its visually dramatic, Noh-based production of ldquo;Medea rdquo; to the Annex at La Mama. (74A E.
4th St. 212-475-7710. Jan.
11-13 at 7:30 and Jan. 14 at 2:30 and 7:30.)
In a weeklong stint at the Joyce, the contemporary-ballet troupe adds intriguing guest choreographers to its usual formula, which consists of Dwight Rhoden rsquo;s attractive but dense choreography, Desmond Richardson rsquo;s knockout solos, and the company rsquo;s sleek, fervid dancing.
Richardson performs an intimate solo created for him by the actor (and Garth Fagan-trained dancer) Taye Diggs. The former company member Jodie Gates contributes a structured-improvisation quartet, and Rhoden offers a first look at his new Marvin Gaye suite, ldquo;Chapters. rdquo; (175 Eighth Ave.
, at 19th St. 212-242-0800. Jan.
9-10 at 7:30, Jan. 11-12 at 8, Jan. 13 at 2 and 8, and Jan.
14 at 2 and 7:30.)
Back in town for the first time since a well-received 2001 appearance, the athletic eight-member company presents a program of four contrasting new works, three of them by Isaacs. In the world premi re of ldquo;Her It Age, rdquo; Isaacs pairs a highly personal exploration of aging with Italian-American songs from her childhood, while the character-driven vignettes of ldquo;Three Quartets and More rdquo; are set to Kronos Quartet recordings of music by Steve Reich.
(St. Mark rsquo;s In-the-Bowery, Second Ave. at 10th St.
212-674-8194. Jan. 11-13 at 8:30.
)
The Philadelphia-based choreographer brings well-constructed dances and a company of eight to the Joyce SoHo. ldquo;Four Songs by Henry Purcell rdquo; is Mark Morris-like, not only in its use of Baroque music but also in its pastoral lyricism, complemented by a touch of irreverence. A quick, bright duet to Bach and a blues-tinged solo to Wayne Shorter flank the premi re of ldquo;Embers, rdquo; which draws an innocence-to-maturity theme from Shostakovich rsquo;s String Quartet No.
11 in F Minor. (155 Mercer St. 212-334-7479.
Jan. 11-13 at 8.)
ldquo;Rounds, the First Last Dance, or the Last First Dance, or an Ordination, rdquo; the protracted title Byrne has chosen for her latest work, refers to the format of the in-the-round piece and to Byrne rsquo;s long-standing interest in the sacraments.
This church service, however, moves to the thrashing rock of the band Hot Young Priest (led by Byrne rsquo;s sister Mary), performed live. Thrusting, caressing, and climbing, the dancers turn a serious game of Twister into a visceral and polymorphous vision of spirituality. (Dance New Amsterdam, 280 Broadway, at Chambers St.
212-279-4200. Jan. 11-13 at 8 and Jan.
14 at 3.)
ldquo;I Love Dan Flavin rdquo; is an homage both to the fluorescent-tube artist and to visions of technological utopia, circa 1980. As they impassively execute precise patterns in chic tracksuits to recordings by the techno band Kraftwerk, the dancers resemble catwalk models, a drill team of zombies, robots on the fritz.
All this retro kitsch is delicious mdash;if hard to take for forty-five minutes. (Dixon Place, 258 Bowery, near Houston St. 212-219-0736.
Jan. 12-13 at 8. Through Jan.
27.
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