Disclaimer: I was really uncertain about posting this question, because it is quite similar to this Algebraic topology beyond the basics: any texts bridging the gap?. I don't know if it would be best to put my question as a comment on Algebraic topology beyond the basics: any texts bridging the gap? or rather create this new question. However, I thought that pheraps it brings to new interesting answers.

Question: I am a PhD student in algebraic topology, and I learned the basics of the subject from some of the many valuable texts suitable for a first course. Now, I am searching for more advanced books which I can keep as a reference for more advanced topics that I might encounter in the future.

To be more precise: suppose we divide the literature on algebraic topology in the following categories:

1. Standard books (e.g. the books by Hatcher, Tammo tom Dieck, Massey)
2. Non standard books: those with a different approach to the subject and that contain some more advanced topics, for example Algebraic topology from an homotopical point of view by Aguilar, Gitler, Prieto (https://www.amazon.com/dp/1441930051) or, even if more advanced, From categories to homotopy theory by Richter (https://www.cambridge.org/core/books/from-categories-to-homotopy-theory/A109E2C4B720337DE19A15EB4FA8C9A6).
3. Advanced books: they contain more advanced topics but they are not monographs, for example: Differential forms in algebraic topology by Bott and Tu (https://www.maths.ed.ac.uk/~v1ranick/papers/botttu.pdf),
   Homotopical topology by Fomenko and Fuchs (https://link.springer.com/book/10.1007/978-3-319-23488-5), A concise course in algebraic topology by May (https://www.math.uchicago.edu/~may/CONCISE/ConciseRevised.pdf) or Generalized cohomology by Kono and Tamaki https://books.google.it/books/about/Generalized_Cohomology.html?id=3HY4ruJ6BigC&redir_esc=y)
4. Monographs: those big books where you can find the details of a specific theory (e.g. K-theory by Atiyah, Operads in Algebra, Topology and Physics by Markl, Shnider, and Stasheff, Rational Homotopy Theory by Felix, Halperin, Thomas)

The books I am looking for are those in the second and third category. So, books that approach algebraic topology from an unusual point of view and/or contains a bunch of more advanced topics.

Other titles would be very welcome, as well as comments about the books I listed above.