Two sides of symplectic topology, rigid and flexible, coexist in constant competition.

The rigid side concerns with developing new  invariants  and constraints, while the flexible side attempts to make constructions which are not yet prohibited. Many outstanding results on both sides of symplectic topology were proven  over 30 years ago, mostly by M. Gromov, when the subject of symplectic topology was created. While in the following years most successes were on the rigid side the situation changed in the last 5 years when many unexpected new results on the flexible side were discovered. In two lectures I will introduce the subject of symplectic flexibility and review its  most recent development.