This talk is an introduction to Nijenhuis Geometry, a new challenging area in Differential Geometry that studies local and global properties of geometric structures given by a field ofendomorphisms with vanishing Nijenhuis torsion. This topic is located on the crossroad of Geometry, Mathematical Physics and Algebra as Nijenhuis structures naturally appear in many seemingly unrelated research areas such as bi-Hamiltonian integrable systems (both finite and infinite-dimensional), projective geometry, theory of left-symmetric algebras and others.

In terms of ideas, methods and tasks, Nijenhuis geometry most of all resembles Poisson geometry, and I will try to emphasise this similarity.