Pigliucci is a philosopher of science by training (Ph.D. in evolutionary biology, second Ph.D. in philosophy of science) who came to Stoicism in midlife and has become one of its most prolific contemporary teachers. He runs the New York Stoa, organizes Stoicon, and writes regularly on the practice for both academic and general audiences.
How to Be a Stoic is the book that won him his audience. Its premise is simple: each chapter is structured as a conversation with Epictetus, with Pigliucci asking the questions a modern reader actually has and Epictetus (via the Discourses and the Enchiridion) answering. The form is not gimmick. It is faithful to how the ancient texts were produced — Epictetus's Discourses are themselves transcribed conversations, and Pigliucci is recreating the encounter in modern context. The book is the most direct working-out of how an intelligent modern reader can sustain a real interlocution with the ancient texts.
A Handbook for New Stoics, written with Gregory Lopez, is the practical companion. It is structured as a 52-week curriculum, with each week introducing one technique, providing the source passages, prescribing a daily exercise, and offering reflective prompts. It is the closest thing the contemporary literature has to a year-long course in lived Stoic practice.
Where Pigliucci is most useful is in his refusal to flatten the harder doctrines. Pop Stoicism tends to drop preferred indifferents, oikeiōsis, cosmopolitan ethics, the theology, and the doctrine of fate as embarrassments. Pigliucci treats them seriously — sometimes critically — and gives the reader the equipment to make their own judgments. He also engages seriously with the question of what aspects of Stoic philosophy are still tenable for someone who does not share the Stoics' theological premises. He himself is a secular Stoic; the philosophical work of separating the load-bearing parts of the system from the historically contingent ones is something he does in public.
He is the writer to read when you want the system, not just the techniques.