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I'm a mathematician and I would like to have a first course on astronomy and/or a first course on cosmology. I'm looking for references that are experiment-oriented, which means that should emphatize observation and experiments, comment them as much as possible and evidentiate how progressively the scientific community made up its mind until the actual state of the art.

I guess this ideal book maybe is a book that is not yet written, but everything that approximates it would be appreciated.

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Well, a book with everything about cosmology and astronomy doesn't exist. I recommend you these "observations-oriented" books:

  • for the extragalactic astronomy: Schneider P. - Extragalactic Astronomy and Cosmology;

  • for the stellar astronomy: Salaris M., Cassisi S. - Evolution of Stars and Stellar Populations.

For the cosmology it is difficult to find a book without some theoretical chapters. I recommend:

  • Coles P., Lucchin F., - Cosmology the origin and evolution of cosmic structure; that is an old, but very intuitive, book.
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