Toda-like systems: solutions and symmetries

This report is consisted of six independent chapters, each chapter (except chapter 1) is a paper carried out in colabouration with others, who's names are indicated in chapter1. The topics included are (1)Overview of general properties of Toda-like systems (chapter1) (2)Free field representations of some particular example of entended Toda like system via Drinfeld-Sokolov construction (chapter2) (3)Heterotic conformal Toda system (chapter3) (4)Heterotic Liouville systems related to Bernoulli equation (chapter4) (5)Two-extended Toda field in three-dimensions--a representative example of extended Toda systems in higher dimensions (chapter5) and (6) $W_N^{(l)}$ algebras in the exchange algebra's framework (chapter6)