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Ten lectures of 2 hours each, including laboratory's experiments by using MATLAB. The purpose of this course is to illustrate and describe the role of trust region strategy in Nonlinear Optimization. The discussion in the first half of the course will be devoted to the trust region algorithms for the unconstrained optimization and nonlinear systems of algebraic equations. In the last half of the course, after a review of the sequential quadratic programming methods for the general nonlinear programming problem, the trust region strategy for the constrained optimization problem is presented. This is a rich and deep topic requiring much more than four lectures to cover with any rigor. Nevertheless, this topic will be introduced highlighting issues that involve optimization. The course concludes by presenting recent developments in algorithms and software for trust region approach. Attendees will obtain an understanding of state-of-the-art in trust region methods for nonlinear optimization problems.