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)

1. Standard books: they contain the basics of algebraic topology (homology, cohomology, homotopy theory) and are usually used in a first class (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).
3. Advanced books: those books that 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), From categories to homotopy theory by Richter (https://www.cambridge.org/core/books/from-categories-to-homotopy-theory/A109E2C4B720337DE19A15EB4FA8C9A6). 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)

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

Edit: I know that the concept of "advanced book" is quite subjective. So, let me try to be more precise as I can: suppose you have learned all the stuff contained in Hatcher's book and now you want to learn something about K-theory. You can either study the book of Atiyah (which is a monograph) or you can take a look for example at the book of May which gives you an overview of the theory that you can pick as a starting point.

So as an advanced book I mean a book that contains some topics that you usually do not learn in a basic algebraic topology class (e.g. spectral sequences, generalized cohomology theories, operads) but at the same time it is not a monography. For example the book of Aguilar, Gitler, Prieto contains some chapters about K-theory and other generalized cohomologies, the book of Fomenko-Fuchs contains something on spectral sequences.

So maybe a more fair question could be: what books would you recommend to a graduate/PhD student in order to get the flavour of some more advanced topic (but still classical) without going in all the details of the theory? Are there some big books that contain a lot of stuff and that one can consult everytime he do not know a specific topic?

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