The Fourth Book is short, and most of its bulk in the editions that circulated is made up of other people's texts bound in with it. What travels under the title is typically a package: the Fourth Book proper, on the making of spirit seals and the practice of evocation; the Heptameron attributed to Pietro d'Abano, on the angels and conjurations of the days of the week; a treatise on geomancy; and shorter pieces on the ecclesiastical and magical orders.
The Fourth Book's own contribution is operative in a way the genuine three books are not. Agrippa describes and theorises; this text tells the reader what to do, and it supplies the missing practical layer that a reader of the Three Books might otherwise go looking for. That is precisely why it was written and attached to his name.
It was denounced as spurious almost at once, most sharply by Johann Weyer, who had been Agrippa's pupil and had an interest in defending his teacher's reputation. Weyer's judgement is the earliest and the best informed, and modern scholarship has not overturned it. The attribution nonetheless stuck, and later occultists generally used the package as a single work.
The package also gave later occultism one of its most reproduced items, the table of the ecclesiastical and magical orders, which sets angelic hierarchies against their supposed opposites and has been reprinted for four centuries.