Optimization methods play a crucial role in kernel methods such as Support Vector Machines and Kernel Logistic Regression. In a variety of scenarios, different optimization algorithms are better suited than others. The aims of the six lectures in this topic are: (1) to introduce a range of optimization problems that arise in the solution of classification problems by kernel methods; (2) to briefly review the relevant optimization algorithms; and (3) to point out in some detail as to which optimization methods are suited for these varied problems.