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A lad falls asleep in a library reading a book about a unicorn only to wake up in a wood to see one. He then meets a cockatrice, manticore, griffon, phoenix and a mermaid(possibly others). The book was read to us at school(1975/6) and illustrated(b&w), each chapter had a new monster- I remember this clearly because the teacher copied them large and me and a schoolmate painted the griffon for the board!