The present issue of Axiomathes introduces a new feature: when the board finds a new book that promises to open new research fields, to present new categorical frameworks or methodologies, a series of papers will be collected discussing the pros and cons of the book, together with replies from the author(s). This new section is in addition to the traditional reviews and critical notices: its aim is to dig more deeply and systematically into the nuances of the book selected for discussion, and to open an early debate on its points of novelty.