On the local relative trace formula

This thesis contains material from approximately three papers. The first chapter is the introduction. The second contains an explicit derivation of the local relative trace formula for the symmetric space F xSL2(F) at the level of Lie algebras. In the third, the author studies one side of the local relative trace formula for a general class of symmetric spaces, by combining results of Arthur and Harish-Chandra with the structure theory of Helminck. In the last chapter, a computation is given that motivates an approach to the other side.