explain the Gromov’s idea how to attach an analytic disk to a Lagrangian submanifold in $\cc^n$;

- in §8.5 we give the proof of his “non-squeezing theorem";

- in §8.6 we study exeptional spheres in symplectic $4$-manifolds.

In Appendix V, following S. Nemirovski, we discuss one more approach to the problem of constructig envelopes of meromorphy of spheres. This approach uses Seiberg-Witten theory. As an example if his results

- we prove that a complex disk cannot be attached from the outside to the strictly pseudoconvex domain in $\cc^2$, which is diffeomorphic to the ball.

The authors would like to give their thanks to Alan Huckleberry, the head of Graduiertenkolleg program at the Ruhr-University and to SFB-236 for the constant support of our joint research. We would like also to give our thanks to Barbara Huckleberry for the uncountable number of grammatical corrections.

[Chapter I. Local Properties of Complex Curves.]{}

In this chapter we shall concentrate on local properties of complex curves in almost-complex manifolds.The first lecture is very basic and mainly defining. Its aim is to introduce a couple of notions and recall a few standard facts. In the second one we prove, following Vekua and Sikorav, the existence 