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As one of the features that Euclid's Elements states, we can build up an entire subject system by simply combining and constructing using a few pieces of axioms, by doing construction of axioms, we can construct theorems, acquire new definitions, and more unknown knowledge we didn't even think about them before.

I am wondering, does there exist books that teaches this kind of "axiomatic approach" thinking? If so, what are them? If not, are there any mathematically related textbooks that have this axiomatic approach features?

Can someone recommends some textbooks that have the above features? Sincerely appreciated.

DigitalSoul
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  • Pick your desired mathematical topic, which I'll denote here by X, and google "axiomatic treatment of X" or "axioms of X" or "axiomatic foundations of X" or any of many similar such searches. – Dave L. Renfro Feb 29 '20 at 08:21
  • " are there any mathematically related textbooks that have this axiomatic approach features?" - I'd say practically any textbook for any 3rd year+ college mathematics course. Several 2nd year courses too, but it is more hit-or-miss yet as to whether the material is presented axiomatically. Real Analysis I is usually an excellent introduction to axiomatic treatment of a subject other than Geometry or Set Theory. – Paul Sinclair Feb 29 '20 at 16:44

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