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I would like to start reading about transcendental numbers. I am familiar with the basics of field theory, number fields, and complex analysis. I have the least exposure to Galois theory. I am looking for books that are suitable for beginners. What are your suggestions?

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    $\begingroup$ 'Irrationality and Transcendence in Number Theory' by David Angell is a very recent book on the subject. $\endgroup$
    – user180579
    Aug 23, 2021 at 5:48
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    $\begingroup$ It looks like the book you mentioned will be released in Feb 2022. I found it in this link. $\endgroup$ Aug 23, 2021 at 6:21
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    $\begingroup$ Transcendental Number Theory by Alan Baker and Transcendental Numbers by C L Siegel. Also do go through the books of Ivan Niven referenced in an answer here. Niven presents the arguments in a fashion which is very easy to grasp. $\endgroup$
    – Paramanand Singh
    Sep 3, 2021 at 15:32
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    $\begingroup$ Disclaimer: I am the author of the book mentioned by @eloiprime. I don't suppose it would be ethical to give it a plug myself, but I hope it is OK if I state that it was published earlier than expected and is now available from all the usual sources. $\endgroup$
    – David
    Jan 20, 2022 at 22:45

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I suggest The following books...they are very great in my opinion ...they are available at internet:

  1. Irrational Numbers Ivan Niven

  2. Numbers Rational and Irrational Ivan Niven

  3. Pillars of Transcendental Number Theory by Saradha Natarajan, Ravindranathan Thangadurai

  4. Transcendental Numbers by M. Ram Murty, Purusottam Rath

  5. Making Transcendence Transparent: An intuitive approach to classical transcendental number theory

(I am telling you the following as advice ...that you should love these numbers.)

I also love transcendental numbers :

I wish to know the solution of the open problem $e+\pi$ ...my self I think $e+\pi$ is transcendental even though it is not bad if it is rational.

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