Got this off Amazon for cheap so I assumed it was the international edition. However the ISBN is of the original Princeton edition but doesn’t match the cover photos nor the price.

As far as I can tell from skimming, the content is all in there so I have half a mind to keep it but I am worried about the longevity of the construction if it’s a counterfeit even if it appears to be a pretty well made one.

Ok, the title isn't exactly accurate--I know that the answer heavily depends on the individual, and on their particular subfield of mathematical interest.

Still, there are some classics that are just so canonical that if you have even a passing interest in the topic, you should be comfortably familiar with its content. I have in mind

• Rudin's Principles

• Munkres' Topology

• Dummit and Foote/Artin/Gallian for Algebra

• Folland for PDEs

• Bak/Churchill and Brown/Ahlfors/Stein and Shakarchi for Complex Analysis

• Rosen's Elementary Number Theory

• Spivak's Calculus on Manifolds

• Maybe arguably Jech's Set Theory for graduate-level Set Theory

• Casella and Berger's Statistical Inference

• Royden's Real Analysis

• Taylor/Marsden/Spivak for Advanced Calculus

• Pearl's Causality

For some of these I'm not sure if there are multiple books which could be considered canon. For others I'm not sure if the number of canonical texts is zero. I personally like Axler's brand new Measure, Integration, and Real Analysis more than Royden's. I find Royden inadequately organized and with lots of mistakes even in the edited version. But I don't think Axler's is known enough yet to replace Royden as the canon.

Are there any other books that could be considered pretty solidly canon in their respective fields?

In particular, as far as I can tell, there is no canon for the fields below. In each case, I am very possibly (in some cases very likely) wrong and just don't know the beloved texts within each field.

Euclidean Geometry (Euclid's Elements isn't modern enough that you could really say that you know Euclidean Geometry from reading it), Combinatorics, Differential Forms, Mathematical Logic (maybe I'm just not appreciating how much Enderton is loved within the field?), Model Theory, Proof Theory, Theoretical Computer Science (Sipser seems to be a fast-growing favorite, but isn't it a little insufficiently rigorous?), Linear Algebra (maybe Axler?), the various subfields of Topology, Category Theory, Projective Geometry, non-Euclidean Geometry, ODEs (maybe Boyce and diPrima but doesn't seem rigorous and comprehensive enough), Measure Theoretic Statistics (maybe Shao, maybe Schervish), Bayesian Statistics (Gelman seems popular but I get the sense it'll be quickly out-dated. Jaynes seems comprehensive but quirky enough that I don't think most Bayesians would accept it as canon.), Nonparametric Statistics (Wasserman?), Order Theory, Algebraic Geometry, Numerical Methods.

I think "canon" should mean some kind of fuzzy mixture of: widely used in relevant courses, loved by most professors, contains the information which is regarded as standard, modern, and comprehensive enough.

The user u/qiling is a crank who likes to flood math and philosophy subs with his nonsense. He has been doing this for years.

He is responsible for the top three posts in this sub right now. This is a small sub, so when he posts here, the post gets elevated in people's feed, despite getting down-voted. There is no reason why his nonsense should be routinely showing up in my front page.

In my opinion, the mods (u/roger_ and u/gmfawcett) should do something about this user. I am speaking for myself, but I will not stay subscribed to any math or science subreddit that allows itself to be dominated by a crank.  

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There is a version of Halmos Naive Set Theory online provided by the Hathri Trust Digital Library in public domain. But their version is a scanned book, and while it is perfectly readable, it is kind difficult to search words with Cntrl + F and there is no interactable summary. So I decided to re-edited the book to improve it, and now it's freely available in my Github repository for download. Besides the visual update and the upgrades in interaction, the final version is only a 400kb pdf!

If someone know other places that I can share this version of the book please share with me, I really love this books and I hope that my version could help spread it to more people