What is a good textbook to learn about infinite-dimensional manifolds?

Question

The goal of this question is to serve as an "abstract duplicate target", as there are currently many different questions on this site about this exact topic.

Which textbooks are there to learn about infinite-dimensional manifolds, for example Fréchet manifolds, Banach manifolds and Hilbert manifolds?

---

There are the following identical questions:

• How are infinite-dimensional manifolds most commonly treated?

• Refrence Request - Book for Manifolds over Banach Spaces

• Reference request: infinite-dimensional manifolds

• Books recommendation: differentiable manifolds, Banach manifolds

• Reference on Infinite Dimensional Manifold

• Help with understanding $L^2(\mathbb{R},\mathbb{R}^n)$ manifolds (?)

• How are infinite-dimensional manifolds most commonly treated? (MathOverflow)

• Infinite dimensional Riemannian geometry (MathOverflow)

Answer 1

There are the following textbooks to learn about infinite-dimensional manifolds:

1. "The Convenient Setting of Global Analysis" by Andreas Kriegl and Peter W. Michor

2. "Functions on Manifolds: Algebraic and Topological Aspects" by V. V. Sharko

3. "Diffeology" by Patrick Iglesias-Zemmour

4. "Fundamentals of Differential Geometry" by Serge Lang

5. "Foundations of Global Non-Linear Analysis" by Richard S. Palais

6. "The Inverse Function Theorem of Nash and Moser" by Richard S. Hamilton

7. "Manifolds, Tensor Analysis, and Applications" by Ralph Abraham, Jerrold E. Marsden and Tudor Ratiu

8. "Foundations of Mechanics" by Ralph Abraham and Jerrold E. Marsden

9. "Analysis, Manifolds and Physics" by Yvonne Choquet-Bruhat and Cecile DeWitt-Morette

10. "Riemannian Geometry" by Wilhelm P.A. Klingenberg

11. "Infinite-Dimensional Lie Groups" by Karl-Hermann Neeb

12. "Nonlinear Functional Analysis" by Klaus Deimling

13. "Real and Functional Analysis" by Serge Lang

14. "Differential and Riemannian Manifolds" by Serge Lang

15. "The Dolbeault complex in infinite dimensions, I." by László Lempert

16. "The Dolbeault complex in infinite dimensions, II." by László Lempert

17. "The Dolbeault complex in infinite dimensions, III." by László Lempert

18. "On the differential geometry of infinite-dimensional Lie groups and its application to the hydrodynamics of perfect fluids" by Vladimir I. Arnold

19. "Geometric Aspects of General Topology" by Katsuro Sakai

20. "Topology of Infinite-Dimensional Manifolds" by Katsuro Sakai