Introduction to stability conditions 1

In 2002, Bridgeland defined the notion of stability conditions on a triangulated category, motivated by string theory and mirror symmetry. Since then, Bridgeland stability conditions have been found very useful not only in Mathematical Physics, but also in various areas of Pure Mathematics.
In the first part, I will review basic background and open problems in the theory of Bridgeland stability conditions. In the second part, I will explain recent developments of the theory, especially its applications to algebraic geometry.