。
She's reading an introductory book on gardening.
Literal
She [topic-は] gardening [genitive-の] introductory-book [object-を] is-reading.
入門書 — literally 'enter-gate-book' — is a 'beginner's primer' for any field. The 入門 ('entry') morpheme appears wherever introductions are offered: 入門編 ('introductory volume'), 入門講座 ('intro course'), and the verb 入門する ('to begin studying / become a disciple'). The image is of crossing a threshold into a discipline — historically a literal one in martial arts and traditional crafts, where new students would 'enter the gate' of a teacher's school. ~ている here marks an ongoing reading session.