Children should play tennis for fun, we're told--and then we hear about the psychological complexities of the game and the merits of competition. Psychologist and pro tennis player Anthony and tennis coach Bollettieri, of 60 Minutes renown, are much concerned with parental input: ""The crux of the problem is the parents' own low self-esteem. A father might think less of himself because he was never the athlete he might have been."" (And then again, he mightn't give a hoot.) Also on the agenda are tennis and a child's mental health, tennis as a personality test, and tennis and the formation of personality (""In adulthood tennis may be just a manifestation of someone's personality, but in childhood it may serve to mold that personality""). Competition, the authors stress, ""promotes excellence""; and along with pointers on playing in tournaments, we have lessons in gamesmanship and emotional control--many of today's stars notwithstanding, children should be taught that keeping cool helps their playing. The heavy counseling aside, there is discussion of equipment (borrow a racquet to start, but good shoes are a must) and where to play (easy in Southern California, but New Yorkers will have a problem). For parents who take their children's tennis seriously indeed.