This Ph.D. thesis is devoted to the application of Stochastic Di erential Equations (SDE) to problems arising in Interest Rates Modelling. The work is part of a large joint project of the IAC-CNR (Institute for the Applications of Calculus of the Italian National Research Council) and the Treasury Department of the Italian Economy and Finances Ministry. The project aims to optimize the Public Debt Management: a brief survey on this complex problem is given in chapter 3. In particular, interest rates play a key role as one of the stochastic components of the corresponding optimal control problem.