Anatoly T. Fomenko has authored and coauthored a number of books on differential geometry and topology. He may be more known for other things, but I have been told his books are quite good for learning geometry and topology. As an undergraduate student planning on learning differential geometry, this piqued my interest. They all seem to be translations of works originally written in Russian. Can anyone compare and contrast them? Here I list them with his coauthors.
Dubrovin, B. A., Novikov, S. P. (1984, 1985, 1990). Modern Geometry — Methods and Applications: Parts 1, 2, 3. Graduate Texts in Mathematics. Springer.
Differential Geometry and Topology. (1987). Consultants Bureau.
Mishchenko, A. S. (1988). A Course of Differential Geometry and Topology. Mir Publishers.
Novikov, S. P. (1990). Basic Elements of Differential Geometry and Topology. Mathematics and Its Application. Kluwer Academic Publishers.
Visual Geometry and Topology. (1994). Springer.
Mishchenko, A. S. (2009). A Short Course in Differential Geometry and Topology. Cambridge Scientific Publishers.
Bonus: His wife also seems to have coauthored a book on topology:
- Borisovich, Yuri G., Bliznyakov, Nikolai M., Fomenko, Tatyana N., Izrailevich, Yakov. A. (1995). Introduction to Differential and Algebraic Topology. Kluwer Texts in the Mathematical Sciences. Kluwer Academic Publishers.
From what I can make of them, book (6) seems to be a trimmed version of (3), and (1) seems to be more geared towards physics despite being a GTM book, but I'm not sure.