Stoicism is a philosophy that is concerned with one question: How to live a good life? It's about being resilient against outside influences, mentally and physically. And about preparing for the worst, keeping death in mind, but being content with whatever happens.
"The Ancient Art of Stoic Joy" is an introduction to the philosophy of stoicism. It's a good primer to then go and read primary sources, like translations of Marcus Aurelius's Meditations, or Lucius Senecas Letters from a Stoic or The Manual for Living.
The people behind Stoicism were a diverse set of characters, from poor paupers and slaves, all the way up to Roman emperors, and this book gives an introduction to their thought and lives and how it all connected together. As such it is a solid introduction, but if you already know a lot of things about Stoicism, this is not going to offer much new insight into the ideas behind it.
Stoicism is a philosophy that tries to answer a single question: How to live a good life?
Stoicism is about finding joy within the moment, even though knowing with utter certainty that both the moment and all that we hold dear and our short lives here on Earth, will come to an end. And that there is going to be pain and suffering along the way. It is also about how to deal with these facts, by keeping death in mind, and cherishing the good and bad things while they last. Yet pushing for the best circumstances possible.
This dichotomy of acceptance, while striving for better circumstances is what is at the heart of Stoicism.
Stoics were quite obsessed with death. Dying a "good" death and facing it with equanimity was one of the highest goals. In a way a part of Stoic philosophy was only about that idea. Conquering the fear of death, by constantly keeping it in mind, envisioning how one turns old and grey, and dies.
Stoicism is not passivity per se. Stoics still act in the world, trying to make it a better place. However they don't care as much about the outcomes, but more about what they can actually influence and change. They focus on their circle of competence – an Idea from the 7 Habits. All of this is very much related to some core ideas appearing across Buddhism, Hinduism and Taoism. Namely those of non-attachment and how life is suffering, as they appear in books as old as the Bhagavad Gita or the Tao Te Ching. There must be something truthful about these beliefs, if people re-discovered them, time and time again, across vast stretches of time.
So again. Good book, as an intro to Stoicism, but if you have read the original texts of the Stoics already, there won't be many new ideas to be found here.