Full Idea
According to Bourbaki, there are three main types of structure: algebraic structures, such as group, ring, field; order structures, such as partial order, linear order, well-order; topological structures, involving limit, neighbour, continuity, and space.
Gist of Idea
The main mathematical structures are algebraic, ordered, and topological
Source
Stewart Shapiro (Philosophy of Mathematics [1997], 5.5)
Book Reference
Shapiro,Stewart: 'Philosophy of Mathematics:structure and ontology' [OUP 1997], p.176
A Reaction
Bourbaki is mentioned as the main champion of structuralism within mathematics.