This is the second of three volumes that originated from a series of lectures in mathematics given to high school students by professors of Kyoto University in Japan. The main purpose of the lectures was to show the beauty of mathematics using material that is accessible to those with little preliminary knowledge. Discussion of the theory of trigonometric and elliptic functions and examination of various aspects of the Poncelet closure theorem illustrates the use of algebraic geometry as a method of studying geometric properties of figures using algebra as a tool. The book was originally published in Japanese in 1995 by Iwanami Shoten, Publishers, Tokyo, Japan. Author and translator information is not given