Hyperbolic Trigonometric Laws Via Identities Of Isometries

In this thesis we derive some hyperbolic trigonometric laws by realizing someidentities of isometries in the upper half-plane model and the hyperboloid model of thehyperbolic plane.The thesis consists of three chapters.In the first chapter we obtain some identities of isometries associated to trianglesin a hyperbolic plane.In the second chapter we realize some identities of isometries in the upper half-plane model, and derive some laws of the hyperbolic trigonometry.In the third chapter we further realize some identities of isometries in the hyper-boloid model and obtain some other laws of the hyperbolic trigonometry.