HARA preferences details I am searching for some exntensive details about HARA preferences.  Where could I find some extensive details for HARA preferences? Something like a textbook or notes
The paper Optimum consumption and portfolio rules in a continuous-time model (Merton (1971)) presents (as far as I know, the initial presentation.
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Next we turn to a paper that discusses the importance of the HARA utility.
The Fundamental Nature of HARA Utility (Perets and Yashiv (2013))

Many models in Economics assume a utility function belonging to the
HARA family. This paper shows that HARA utility is fundamental to
economic analysis. The HARA functional form is the unique form which
satisfies basic economic principles in an optimization context. Using
HARA is not just a matter of convenience or tractability but rather an
essential restriction....

This notable paper has a multi page exploration of the HARA utility family.
Implications of Constant Risk Aversion (Bamberg and Spremann (1981))

The assumption of constant risk aversion often leads to a considerable
simplification of decision theoretic analyses. It is shown that this
restriction on constant risk aversion permits the description of a
wide range of risk averse patterns between the extreme cases of risk
neutrality and the exclusive orientation on the pessimistic maxmin
criterion. In particular, a new axiomatic foundation of the constant
risk aversion is given and a series of properties for the certainty
equivalent are derived. Possible applications are shown by the
treatment of risk premiums, values of information, portfolio
selection, capital market theory and syndicates.

There is a book that I can't vouch for but may be useful:
Hyperbolic absolute risk aversion: Second Edition