Surveys, textbooks, and Lecture notes:
[Cieliebak-Eliashberg] From Stein to Weinstein and Back
Kai's notes (taken from the book with Eliashberg) from Budapest on Stein Manifolds: http://www.renyi.hu/~cast2012/stein.pdf
[Hofer-Zehnder] Symplectic Invariants and Hamiltonian Dynamics
[Oancea] A Survey of Floer Homology for Manifolds with Contact Type Boundary or Symplectic Homology
[Salamon] Lecture notes on Floer homology
[Seidel] A biased view of symplectic cohomology
[Wendl] A Beginner's Overview of Symplectic Homology
Research papers:
[Abbondandolo-Schwarz] On the Floer homology of cotangent bundles
[Cieliebak] Subcritical manifolds are split
[Eliashberg-Gromov] Convex symplectic manifolds
[Oancea-K] The Kunneth formula in Floer homology for manifolds with restricted contact type boundary
[Ritter] Topological quantum field theory structure on symplectic cohomology
[Viterbo] Functors and computations in Floer homology with applications. I Warning: It might be better to find the GAFA publication, in which the figures are displayed.