Geometry of involutions

This thesis is consisting of four chapters. In the first chapter; the historical background of subject is expressed. In the second chapter; fundamental definitions and algebraic properties related to real quaternions and real-split quaternions are given. In the third chapter; rotations in Minkowski space E_1^3 are given by using real-split quaternions. In the fourth chapter; two involution and two anti-involtion transformations are given. Moreover, the geometrical meanings of the vector parts of these transformations are given in three-dimensional Euclidean space R^3 or in Minkowski space E_1^3. Finally, the matrices corresponding to these transformations are obtained.