Integrable systems admit various kinds of solutions. In this talk, I will
mainly focus on the molecule solutions and matrix integral solutions. At rst, I will
talk about how to obtain molecule solutions from Toda-type equations and some of
the applications will be addressed. Then I will demonstrate how to generate matrix
integral solutions to a whole hierarchy from molecule solutions of relevant Toda lattices
as a particular application. This talk is based on several works collaborating with
Xiangke Chang, Xingbiao Hu and Chunxia Li.