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**Applications of Category Theory**

`Ovsienko Serge` (Kiev
Taras Shevchenko University)

In our lectures we will expose (relatively) new algebraic
methods, which were effectively applied in surprisingly various branches
of mathematics. We explain, how this phenomenon relates with a unifying
role of the notion of a category and its generalizations. Especially, we
fix our attention on the theory of descent and its applications. Besides,
it will be shown, how such approach can lead us to the "representation-theoretic"
point of view. We will give examples, how the methods above are used in
algebraic and differential geometry, differential equations and physics.