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There are many books which address specific philosophical aspects of Advaita in an academic manner. Most of these are probably only attractive to those actually studying the subject at university but some are so well written and approachable and contain so much useful background material that they are worth attempting by anyone wanting to understand Advaita.
'Methods of Knowledge According to Advaita Vedanta' by Swami Satprakashananda. The cover description states: “The book deals with an exposition of the six means of valid knowledge leading to Self-realization”.
This is excellent - very readable, yet comprehensive and authoritative. I have not come across such lucid explanations of the most abstruse aspects of Advaita before. It also explains the differences between Advaita and other branches of Indian Philosophy. Everything is set out in point by point explanation. And it has probably the most comprehensive index of any book I have seen! (Buy US or UK)
The hardback currently costs around $9, second hand from Amazon.com and about $1, brand new, from Motilal Banarsidass!
The Method of the Vedanta: A Critical Account of the Advaita Tradition by Swami Satchidanandendra, translated by A. J. Alston.
This is a huge book, requiring considerable commitment but, if you want to understand clearly what Shankara believed and how his message has been modified or even distorted by subsequent interpreters, then it is indispensablel reading. Shankara's essential method is presented as that of adhyAropa - apavAda, attribution and subsequent denial. His commentaries on the prasthAna traya are examined in detail. Then, following a brief look at pre-Shankara Advaita, there are chapters on each of the major teachers and schools that followed him, in which the same topics are re-examined and the differences outlined.
Fortunately, the translation is by A. J. Alston - see the Shankara 'Source' books - so is always understandable. This book will be republished by Shanti Sadan when existing supplies run out so that they are the point of contact if you are unable to obtain it.
(Buy US or UK)
Eliot Deutsch - Advaita Vedanta: A Philosophical Reconstruction
This reads like an academic Western Philosophical text and presents Advaita from an objective analytical viewpoint. This might tend to put off many potential readers but should not necessarily do so. Whilst it may seem dry at times and does require some effort to read, it presents some difficult concepts in a very clear manner and is an essential addition if you are building a library of key texts on the philosophy. It is another 5* recommended buy from Amazon.
(Buy US or UK)
"The second theory (which is associated with the Bhamati school of Advaita) is called avaccheda-vada, the theory of limitation. According to this theory, consciousness that is pure and unqualified, without sensible qualities, cannot be 'reflected', and hence the analogy with the mirror breaks down when pressed to the point which the pratibimba-vada takes it."
The Method of Early Advaita Vedanta: A Study of Gaudapada, Sankara, Suresvara and Padmapada by Michael Comans
This is a great book by a PhD student of Swami Dayananda who's also a teacher of Vedanta and Sanskrit in Sydney Australia. Not only does he examine teachings of Gaudapada and Shankara, but also Suresvara and Padmapada. He also gives a great contrast to the teachings of Advaita Vedanta and Madhyimaka and Yogacara in the section on Gaudapada. Recommendation by E. J. Shearn
I have finally got around to reading this
myself (Sept. 2008) and here is my review:
I had been aware of the existence of this book for a number of
years but had postponed reading it because I was under the impression
that it was of only academic interest, comparing the finer details
of various schools or teachers. In fact, although there is a
little of this (e.g. in comparing Gaudapada’s teaching
to aspects of Buddhism), its strength for me is in its detailed
examination of some particular aspects of traditional advaita.
Topics specifically addressed are Ishvara, jIva, upAdhi, nAma
rUpa, avidyA, adhyAsa, lakShaNa, immediate versus mediate knowledge
and experience, jIvanmukti, saMnyAsa, anvaya vyatireka – and
their treatment is extremely clear and informative.
The chapters on Sureshvara and PadmapAda
were also very enlightening for me personally,
since I had not previously investigated
them. In the case of the former, he provides
an analysis of the naiShkarmya siddhi which
is so interesting that I was prompted to
order the translation by A. J. Alston (‘Realization
of the Absolute’) immediately. In
the case of the PadmapAda, he presents
a valuable analysis of his commentary on
Shankara’s adhyAsa bhAShya.
All in all, this is an excellent book,
which is highly recommended for anyone
who, though already familiar with the topics
in a general way, wants to understand them
in greater depth. It does seem that, as
soon as you look in greater detail into
something that you thought you understood,
you discover that there is much more to
it than you had thought and perhaps you
didn’t understand it properly after
all. Michael Comans’ book takes you
deep into the undergrowth but guides you
carefully out the other side.
(Buy US or UK)