''Not Quite a Horsewoman'' has, since its publication in 1982, delighted thousands of aspirant riders and horse owners. Now in its third edition and embellished with even more delightful cartoons by Anne Pilgrim, it will entertain a new generation of horse lovers as Caroline Akrill reveals the frequent disasters and the occasional triumphs of her long association with a string of equine characters. Ambitions and aspirations fall by the wayside as she tells the story of her leading rein pony, the saga of her show hack and the tale of her season as a hunting columnist. She remembers her first stable yard where she was exploited by her own working pupils, her brief career as a dealer operating from a small village pub, and the agonies of professionally producing show ponies as their owners waited at the ring-side with their livery cheques still unwritten. Engagingly witty, endearingly frank, sometimes surprising, but always amusing, Caroline Akrill regards the horse from the safety of the stable door and scrutinises him with candour and affection.