Shaw's work refracts the divine light of Iamblichus' system to allow it to shine again in an era when such wavelengths have become invisible. In so doing, he convincingly explains the esteem in which Iamblichus was held for a millennium (second only to Plato).
That reputation was built upon a unified cosmic vision that both (a) provides an active role for all people, not just a contemplative elite, and (b) avoids the gnosticizing pitfalls of some Platonic worldviews which denigrate the material cosmos or set the individual soul against the created order. In Shaw's telling, theurgy is the practical application of a doctrine of a participatory and interrelated universe where synthemata link various herbs, animals, stones, planets, etc. to certain gods in an imbricated hierarchy stretching all the way up to the One. Because of those connections, there is a theurgical practice for every soul's station: material sacrifices elevate the common man's soul, while noetic sacrifices do the same for the philosopher. Shaw convincingly links Iamblichus' program to Pythagorean number mysticism but democratized to allow a role for even the neophyte.
It's easy to understand the appeal of this approach in late antiquity since it rescues pagan cultic practice and a venerable philosophical tradition, while competing with popular religions of individualized salvation like Mithraism and Christianity. Shaw's account really elucidates the stakes in the debate between Plotinus/Porphyry and Iamblichus on the undescended soul while also defending Iamblichus from charges of irrationalism or fetishism. He also notes briefly how the Catholic Church became a repository of much of the Iamblichean cosmic vision, although I would welcome a deeper exploration of that topic. I'm less familiar with Iamblichus than many other Platonists but this volume was a wonderful introduction and a highly sympathetic reading. Shaw is a clear writer and his enthusiasm for the subject shines through the text. Highly recommended.