The course will cover the basics of strong logics, such as generalized quantifiers, infinitary logic and second order logic, especially from the point of view of interaction between model theory and set theory. An example of a generalized quantifier is the quantifier "There are uncountably many". In infinitary logic we allow infinite disjunctions and conjunctions. In second order logic quantification over subsets of the domain is allowed. Strong logics can express mathematical properties that go beyond first order logic, such as connectivity of a graph, torsion-freeness of an abelian group, finiteness of a predicate, etc. In general, set theoretical methods are needed in developing model theory of strong logics. On the other hand, strong logics give rise to interesting set theoretical questions, such as large cardinal properties and reflection principles.