Symplectic Manifolds with no Kaehler structure

This is a research monograph covering the majority of known results on the problem of constructing compact symplectic manifolds with no Kaehler structure with an emphasis on the use of rational homotopy theory. Some stimulating conjectures and problems have been formulated due to an influx of homotopical ideas. Examples include the Lupton-Oprea conjecture and the Benson-Gordon conjecture, both of which are in the spirit of some older and still unsolved problems (for example Thurston's conjecture and Sullivan's problem). The aim of this text is to clarify the interrelations between certain aspects of symplectic geometry and homotopy theory in the framework of the problems mentioned above. The reader is expected to be aware of the basics of differential geometry and algebraic topology at graduate level.