Here are some links to books, lecture notes and survey papers that cover in depth some of the topics mentioned in the blog. Feel free to post suggestions in the comments and we’ll add them to the list.

4-manifolds, Selman Akbulut

A beginner’s guide to Fukaya categories, Denis Auroux

Stein structures: existence and flexibility, Kai Cieliebak and Yakov Eliashberg

Legendrian and transverse knots, John Etnyre

Lectures on contact geometry in low-dimensional topology, John Etnyre (covers (1) foliations and contact structures (2) symplectic handles (3) open book decompositions (4) symplectic caps)

Lectures on open books decompositions and contact structures, John Etnyre

Lectures on knot homology and quantum curves, Sergei Gukov and Ingmar Saberi

Lectures on embedded contact homology, Michael Hutchings

Notes on bordered Heegaard Floer homology, Robert Lipschitz, Peter Ozsvath, Dylan Thurston

Topological methods in 3-dimensional contact geometry, Patrick Massot (convex surface theory)

Higher dimensional contact topology via holomorphic disks, Klaus Niederkruger

A topological introduction to knot contact homology, Lenhard Ng

Geometric decompositions of almost-contact manifods, Francisco Presas

Textbooks:

From Stein to Weinstein and Back: Symplectic Geometry of Affine Complex Manifolds, Cieliebak and Eliashberg

Introduction to the $h$-Principle, Eliashberg and Mishachev

Knots and Links, Rolfsen

4-Manifolds and Kirby Calculus , Gompf and Stipsicz

Monopoles and Three-Manifolds Kronheimer and Mrowka

Introduction to Symplectic Topology McDuff and Salamon

J-Holomorphic Curves and Symplectic Topology McDuff and Salamon

Quantum Fields and Strings: A Course for Mathematicians, Deligne, Etinghof, Freed, Jeffrey, Kazhdan, Morgan, Morrison, Witten

Conformal Field Theory and Topology, Toshitake Kohno

Chern-Simons Theory, Matrix Models, and Topological Strings, Marcos Marino

Mirror symmetry, Clay Mathematics monographs

Quantum Mechanics for Mathematicians, Leon Takhtajan

Supersymmetry and Supergravity, Julius Wess and Jonathan Bagger

Introduction to Superanalysis F.A. Berezin

The Wild World of 4-Manifolds, Scorpan

Notes on Seiberg-Witten Theory, Nicolaescu

Pingback: Resources page | The Electric Handle Slide

Hello,

Could you add some material for connections to Physics and some beginner’s lecture notes there.

Regards,

Vijay

I don’t know much about connections to physics, except small bits of ad-hoc intuition I’ve occasionally picked up. I found Takhtajan’s book “Quantum Mechanics for Mathematicians” to be really good. But I think connections to physics generally fall outside the scope of this blog.

I am very fan with this kind of learning, i am just asking for you to add

D. Rolfsen, Knots and Links, AMS Chelsea Publishing, AMS (1990)

Pingback: Contact Hamiltonians (Introduction) | The Electric Handle Slide