'Gillian' explores family tragedy with care and compassion; To Gillian on Her 37th Birthday. Play by Michael Brady, Directed by Pamala Berlin.

''To Gillian on Her 37th Birthday'' employs pathos and comedy to explore the effects of a tragedy's anniversary on a mixed-generational group of characters. Michael Brady is a caring playwright who shares the concerns of the adults and young people he has assembled in the resort area of a small New England coastal island.

The birthday of the title character is being observed rather than celebrated, for it commemorates the day on which a sailboat excursion ended fatally for Gillian, the wife of college professor David (David Rasche). David thereafter retired from teaching and became a permanent island resident. Since the middle-aged widower has included pre-college daughter Rachel (Sarah Jessica Parker) in his determined retreat, the resulting situation has become a matter of concern to Rachel's Aunt Esther (Jean De Baer), the dead woman's sister.

The predictability of ''To Gillian . . .'' emerges early on. Esther and husband Paul (Richmond Hoxie) arrive on the island with fellow guest Kevin (Frances Conroy), a divorced single parent who was once one of David's students.

But Mr. Brady is more interested in character interplay and expressive dialogue than in literal plotting. He treats his characters with the respect and compassionate discernment they deserve. The sympathetic approach applies as much to the slightly pedantic David as to his abrasive sister-in-law, his very bright but troubled young daughter, and to the teen-ager next door (Noelle Parker), who has developed a crush on the reclusive academic.

There is nothing dishonorable about David's behavior. What Mr. Brady gradually reveals is the self-absorption involved in the widower's grief. Even the idealized Gillian, with her independence and her achievements in anthropology, turns out to have displayed quite a lot of self-centered willfulness. Rather than assuming an accusative tone, however, playwright Brady prefers to observe and record. His skills in both departments are impressive.

''To Gillian . . .'' is acted with appealing sensitivity under Pamela Berlin's direction. Mr. Rasche's portrayal of the antisocial David is balanced by Miss Conroy's charm and quiet reserve as the ex-student confronting an emotional crisis for which she has not been prepared. The impressive cast at the downtown Circle in the Square also includes Cheryl McFadden as Gillian's ghost. Introduced into an otherwise realistic situation, revenants (ghosts) can be a tricky business. ''To Gillian . . .'' is no exception. Miss McFadden handles the trickiness with a common-sensical blend of the ethereal and the pragmatic.

Robert Thayer has designed a sky-canopied, beachfront-cum-weathered-cottage setting that spells enchanted escapism. The production has been atmospherically lighted by Allen Lee Hughes and modishly costumed by Deborah Shaw. Composer Robert Dennis's delicate arpeggios set the musical tone for this well-bred social comedy in a traditional mode.

'Carmen' in English

Performed in its French adaptation since opening last November at the Vivian Beaumont Theater (cq), Peter Brook's unorthodox ''La Tragedie de Carmen'' is now available four times a week in an English version. The Sheldon Harnick translation is presumably faithful to the streamlined libretto by Marius Constant, Jean-Claude Carriere, and Mr. Brook. In any case, it runs smoothly and will make the condensation more accessible, thereby perhaps widening its appeal.

The fateful tragedy was well and clearly sung at a recent press preview by one of the several casts entrusted with the exacting demands of the action-filled music drama. The principals were Cynthia Clarey (Carmen), Howard Hensel (Don Jose), Agnes Host (Micaela), and John Rath (Escamillo). A noticeable feature of the Anglicized version was its greater comic accent - epitomized by Andreas Katsulas's clowning as Lillas Pastia. The tragedy of Carmen threatened briefly to degenerate into the burlesque of Carmen. But fortunately not for long. Randall Behr conducted the stirring musical performance.

The strengths of the production still reside in Mr. Brook's masterful integration of all its parts - the swift flow of the narrative in this shortened version, the emotional intensity of the confrontations and their fatal consequences, and the sand-and-gravel-covered circle of playing space designed by Jean-Guy Lecat to accommodate the headlong action. The ''Carmen'' collaborators have taken bold liberties with Bizet's score. But they have kept their own faith with the melodic structure and invention that sustain and forward the tragedy.