Cohomological aspects of non-K\"ahler manifolds

In this thesis, we study cohomological properties of non-K"ahler manifolds. In particular, we are concerned in investigating the cohomology of compact (almost-)complex manifolds, and of manifolds endowed with special structures, e.g., symplectic structures, D-complex structures in the sense of F. R. Harvey and H. B. Lawson, exhaustion functions satisfying positivity conditions.