What is topology and mention its various types?

Geodatabase Topology: is a collection of rules that, coupled with a set of editing tools and techniques, enables the geodatabase to more accurately model geometric relationships. ArcGIS implements topology through a set of rules that define how features may share a geographic space and a set of editing tools that work with features that share geometry in an integrated fashion. A topology is stored in a geodatabase as one or more relationships that define how the features in one or more feature classes share geometry. The features participating in a topology are still simple feature classes—rather than modifying the definition of the feature class, a topology serves as a description of how the features can be spatially related.Map topology: is a topological relationships between the parts of features that are coincident, which allows you to simultaneously edit features that share geometry. You can create a map topology for point, line, or polygon layers from shapefiles or geodatabase feature classes. The features can be in one or more layers and have different layer types.