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There are many different translations and commentaries on this classic work, where 'many' = tens if not hundreds. Some merely translate the Sanskrit, with varying degrees of accuracy and artistic licence. Others provide several pages of commentary on each verse. I have only 9 different versions so it is perfectly possible that many of those I have not seen are excellent.
The most authoritative version is probably the one that includes all of Shankara's commentaries - translated by Alladi Mahadeva Sastry. Unfortunately, though undoubtedly authoritative, it is not the most readable. Although I would unhesitatingly recommend it to serious students, beginners would almost certainly prefer one of the others below. (Buy US or UK)
Swami Dayananda has written 'The teaching of the Bhagavad Gita'. This is really using the Gita to present an overview of Advaita and it gives verses as illustrations rather than covering the entire book, verse by verse. It is, nevertheless, a very good book and I can thoroughly recommend it. (Indeed, anything by Swami Dayananda can be recommended.) He also provides a study course on the Gita, using extensive notes, which are excellent (available from this site).
(Buy US or UK)
Winthrop Sargeant has a version without Commentary, which has both original and Romanised Sanskrit, together with the meaning and grammar for each word. A number of pages may be read at Amazon.com. (Buy US or UK)
Swami Chinmayananda has a voluminous edition published by Chinmaya Publications. Unfortunately, I have not yet read this so cannot make any positive statements. It looks likely to be very good, albeit possibly a little verbose. It does suffer from a slight drawback in not having the original Sanskrit presentation of each verse. This is also available for free download - see Free Books.
A supremely
readable commentary for the modern reader
is “The
Living Gita” by Sri Swami Satchidananda.
Strictly speaking, this is Yoga rather
than Advaita but that really does not matter
- it is full of clearly expressed wisdom.
If you want to discover the essential message
of the Gita and its relevance to modern
life (and enjoy the reading experience
too) this is definitely the book you should
get. (Buy US or UK)
For a modern treatment, I can recommend this version from Alan Jacobs. It is not a straight translation - the title is 'The Bhagavad Gita: A Poetic Transcreation' - and the verses themselves are updated into a modern, yet evocative free-verse form. Much more than this, however, Alan has biased the wording towards a clearer Advaitic expression. And he has provided a commentary which draws upon his extensive experience of Advaita and incorporates valuable quotations and observations from others, such as Ramana Maharshi and Ramesh Balsekar. Extremely readable, too!
(Buy US or UK)
Read an excerpt here on the subject of reincarnation.
If I had to choose just one version, I would probably pick the version with commentary by Swami Chidbhavananda. Each verse is given in Devanagari, followed by Romanised Sanskrit and then a word for word translation. A full commentary is then given, often using excellent metaphors. Frequently, relevant quotations from Sri Ramakrishna are then presented. This book is available from Blue Dove.
Link to the Advaita Bookstore to read other reviews of these books, buy them from Amazon.com or generally browse.