Control theory provides a large set of theoretical and computational tools with applications in a wide range of fields, running from ”pure” branches of mathematics, like geometry, to more applied areas where the objective is to find solutions to ”real life” problems, as is the case in robotics, control of industrial processes or—nance. The ”high tech” character of modern business has increased the need for advanced methods. These rely heavily on mathematical techniques and seem indispensable for competitiveness of modern enterprises. It became essential for the financial analyst to possess a high level of mathematical skills. C- versely, the complex challenges posed by the problems and models relevant to—nance have, for a long time, been an important source of new research topics for mathematicians. The use of techniques from shastic optimal control constitutes a well established and important branch of mathematical—nance. Up to now, other branches of control theory have found comparatively less application in—n- cial problems. To some extent, deterministic and shastic control theories developed as different branches of mathematics. However, there are many points of contact between them and in recent years the exchange of ideas between these fields has intensified. Some concepts from shastic calculus (e.g., rough paths) havedrawntheattentionof the deterministic control theory community. Also, some ideas and tools usual in deterministic control (e.g., geometric, algebraic or functional-analytic methods) can be successfully applied to shastic c- trol.