Peter often recommends Mindfulness In Plain English by Bhante Gunaratanato as a primer for understanding and beginning Buddhist meditation practice.
Here is a video presented by Richard Shankman on the cultivation of samadhi and the jhanas. He is also the author of the book The Experience Of Samadhi, which can be downloaded free.
Small Boat, Great Mountain, by Ajahn Amaro, a Westerner, describes the similarities between the teaching of the Theravada monk Ajahn Chah and the Tibetan meditative discipline, dzogchen. Peter has read it twice, with great benefit.
Inner Listening by Ajahn Amaro, describes the practice used by Ajahn Sumedho, another Westerner. The meditation practice focuses on the inner sounds as a primary object of meditative focus other than the breath. Since Peter has tinnitus, it is another tool he uses to stay present.
Peter sat a jhana retreat with Leigh Brasington many years ago, and he finds his website to be a very useful resource. He particularly values the page dedicated to jhana practice, as well as the listing of recommended reading provided.
Right Mindfulness-Memory And Ardency On The Buddhist Path by Thanissaro Bhikkhu, a Western monk who is well respected for his many translations of Buddhist suttas. This book is about the Four Foundation of Mindfulness, and provides a very insightful view of the terms that recur in the sutta.
Ajahn Chah was a very influential Thai Buddhist meditation master who taught many Westerners, including Ajahn Sumedho and Jack Kornfield. This is a collection of many of his talks that Peter has found to be useful and inspirational.
Analayo has written a classic book entitled Satipatthana-The Direct Path To Realization. As far as I know, this isn’t yet offered as a free ebook. However, here are two books of commentary that I find useful:
Here’s an online glossary of Buddhist terms that can be downloaded in pdf format
Thanissaro Bhikkhu translated a compilation of the teachings that the Buddha is said to encapsulate the path to awakening. It is called The Wings To Awakening: An Anthology From The Pali Canon.
The Anapanasati Sutta is one of the most important teachings in the Pali Canon. Anapanasati is translated as “mindfulness of breathing.” This book, Anapanasati by Buddhadassa Bhikkhu, is considered to be a modern classic commentary on this practice.
Keeping The Breath In Mind & Lessons In Samadhi is another modern commentary by a revered monk, Ajaan Lee Dhammadharo, and provides useful support for deepening understanding of the “craft” of awakening:
Bhante Gunaratana is a Sri Lankan monk who has resided in the U.S. for decades. He has a PhD. In Comparative Religions,and this book, A Critical Analysis Of The Jhanas In Theravada Buddhist Meditation is his doctoral dissertation.
Bhikkhu Bodhi is an American monk who was at one time the editor of the Buddhist Publication Society (BPS, if you want to Google it) and is a well-respected translator of Buddhist texts. Here is his rendering of The Noble Eightfold Path: The Way To The End Of Suffering.
There are many more ebooks on Urban Dharma website, which has been a primary source of downloadable documents for this list.