This manuscript is a note of lectures in the workshop "Combinatorial Quantum Method in 3-dimensional Topology" held in Oiwake Seminar House of Waseda University in the end of September, 1996.

The manuscript is based on the notes written in tex files and the pictures depicted in post script files by the following graduate students; Takuji Nakamura, Tsutomu Nakatsuru, Tatsuya Yagi, Takeshi Yamauchi for Sections 0 to 2, Hiromasa Okuno, Takashi Takamuki, Masato Yamada, Ryosuke Yamamoto for Sections 3 to 5, Atusi Koike, Hideaki Nisihara, Ichiro Torisu, Yoshihiko Tsujii for Section 6, Takayuki Morifuji, Tomoe Motohashi, Miyuki Okamoto, Tatsuya Tsukamoto for Sections 7 to 8. In particular, T. Nakatsuru managed electric operations in computer network by making a mailing list and a home page for this lecture note, and T. Yagi revised many pictures in post script files. I am grateful to them; this manuscript would not be completed without their helps.

I would also like to thank Jun Murakami, Toshie Takata for valuable discussions and comments, Michihisa Wakui for refereeing an early draft, Thang Le for pointing out mistakes in an early draft, and the organizer of the Oiwake workshop, Hitoshi Murakami for giving me a chance to give the lectures and taking case of everything. I am also grateful to the referees for helpful suggestions and comments.

I also thank International Institute for Advanced Studies for warm hospitality in a small workshop in December, 1996.

This research is supported in part by Grand-in-Aid for Scientific Research on Priority Area 231 “Infinite Analysis”, The Ministry of Education, Science, Sports and Culture.

Tomotada Ohtsuki