In accordance with the tendency of Modern Mathematics laying emphasis on Mathematical structure, that is, on axioms, it is necessary for students to be interested in structure of Geometry on Mathematics Education. In fact, it is of importance not only to obtain new ideas but also to forget old ones in the development of Mathematics. Most students do not understand the Mathematical significance of axioms, and do not know what Mathemetical truth is. Now Non-Euclidean Geometry offers opportunity to understand the essence of Mathematics better, and is no less effective than Euclidean Geometry in training student in logical inference. This thesis is a study with regard to what should be taught and how student should be guided at High school Mathematics. Chiefly Hyperbolic Geometry is discussed in connection with Abosolute Geometry. As Non-Euclidean Geometry has not appeared in our curriculum, some experiments are required before putting it into actual curriculum to find out how much students understand and how much pedagogically useful it can be. This is only a. presentation of a tentative plan, which needs to be criticized by many teachers.