American-Jewish food is not on the whole brilliantly represented in the current cookbook literature. Part of the trouble is that kashruth, or observance of the dietary laws, doesn't explain what made one's grandmother's cooking ""Jewish."" So it's encouraging to find a writer as qualified as Mimi Sheraton addressing herself to this amiable but slippery culinary heritage. Moving informally between recipes and good-natured recollections (some of which have appeared in the New York Times), she evokes the ambience of the Flatbush kitchen presided over by her mother, mistress of a ""Polish-Rumanian-Austrian-German-Hungarian"" repertory that also left room for fried oysters and succotash. Some of Beatrice Solomon's recipes are beautiful classics presented with no nonsense: her simple and savory chopped chicken livers, her delightful scharfe fisch (a jellied sweet-and-sour dish), her scrambled eggs with brains, her mushroom-flavored schav (sorrel soup). Some are once-familiar ideas which now have the force of charming novelties, like a sandwich of coarsely chopped radishes, cucumbers, and scallions on pumpernickel, or another with a sort of cheese-blintz filling French-toasted between slices of challah. For baking specialities (strudel, rugelach, Hamantaschen) Sheraton turns to the legacy of her maternal grandmother, ""the best home baker I have ever known."" Many or most of the Solomon family standbys are to be found, sometimes in quite good versions, in other cookbooks--though one often has to sift through a lot of deadwood which is mercifully absent here. The advantage of this collection is the insight it offers into the thinking of gifted individual cooks at work. The strictly kosher can use the book with circumspection; the rest of us from sometime Jews to Presbyterians can embrace it with unreserved pleasure.