The structure-function relationship of the polysaccharides from the view point of the rheological characteristics in aqueous solutions has been insighted into when I was listening to the first movement of the piano sonata No. 14, Op. 27 2, entitled Moon-light which was composed by Ludwig van Beethoven on July in 1973. At that time, I was a doctoral student at the Department of Food Science and Technology, Kyushu University. After getting job at the University of the Ryukyus in 1982, it has been investigated. Gelation mechanism for κ-carrageenan, ι-carrageenan, agarose (agar), gellan gum, alginic acid, curdlan and amylose has been analyzed, respectively, at the molecular level where sulfate oxygen, ring oxygen, hemiacetal oxygen, cations, hydroxyl groups oriented at axial, and methyl groups take part in the intra-and intermolecular associations with ionic bonding, electrostatic forces of attraction, hydrogen bonding and van der Waals forces of attraction. Co-gelation mechanism of xanthan with galactomannan (locust bean gum, tara bean gum, guar gum and Leucaena galactomannan), and with konjac glucomannan, where trisaccharide side-chains of the former molecules contribute with hydrogen bonding has also been analyzed, respectively. The structure-function relationship for non-gelling welan, rhamsan, S-657, S-88, S-198, shizophyllan and amylopectins (rice, potato and wheat), the structure of which is similar to that of gelling gellan, curdlan and amylose has been analyzed. The gellan family of the polysaccharides, as metioned above, have given a good opportunity to investigate the molecular origin for their rheological characteristics. Recently, we have analyzed a gelatinization and retrogradation mechanisms of rice, potato and wheat starches. From the results and discussions, the principles of the polysaccharide gels have been established. Though many investigations concerning the gelling properties of the polysaccharides have been done to discuss structure-function relationship, no one has established gelation mechanisms at the molecular level except the author. There is reasonable consistency in our investigations. Thus, rheological analysis is one of the most significant methods to realize the structure-function relationships of polysaccharides in aqueous solutions. We have isolated a novel fucoidan, which substituted an acetyl group, from commercially cultured Cladosiphon okamuranus in Okinawa, Japan and has been covered by a patent. The fucoidan has an excellent flow characteristics and immunological activity. The fucoidan has now been used in food and cosmetic industries, production of which increases year by year.