# Algebraic Approaches to Graph Transformation, Part I: Basic Concepts and Double Pushout Approach

The algebraic approaches to graph transformation are based on the
concept of gluing of graphs, modelled by pushouts in suitable
categories of graphs and graph morphisms. This allows one not only to give
an explicit algebraic or set theoretical description of the
constructions, but also to use concepts and results from category
theory in order to build up a rich theory and to give elegant proofs
even in complex situations.
In this chapter we start with an overwiev of the basic notions common
to the two algebraic approaches, the "double-pushout (DPO) approach" and
the "single-pushout (SPO) approach"; next we present the classical
theory and some recent development of the double-pushout approach. The next
chapter is devoted instead to the single-pushout approach, and it is closed
by a comparison between the two approaches.
--
This document will appear as a chapter of the "The Handbook of Graph Grammars.
Volume I: Foundations", G. Rozenberg (Ed.), World Scientific.