Aspects of structural combinatorics - (Graph homomorphisms and their use)

This paper is based on a course delivered by the author at NCTS, National C hiao Tung University,Taiwan in February 1999. We survey results related to structural aspects of graph homomorphism. Our aim is to demonstrate that th is forms today a compact collection of results and methods which perhaps de serve its name : structural combinatorics. Due to space limitations we conc entrate on a sample of areas only: representation of algebraic structures b y combinatorial ones (graphs), the poset of colour classes and correspondin g algorithmic questions which lead to homomorphism dualities,blending algeb raic and complexity approaches.