Maple is a general-purpose computer algebra system with very large audience among the world. The RegularChains library in Maple organizes its functionalities into a two-level user-interface. The first level provides the basic functionalities easy to use for the non-expert. Those functionalities allow to compute triangular decompositions and manipulate polynomials. The second level of the user-interface provides more technical functionalities that are available through optional arguments of the basic functionalities and through two submodules, called ChainTools and MatrixTools. Those two sub-libraries respectively provide tools for manipulating triangular decompositions and regular chains, and for doing linear algebra over non-integral domains. This makes Maple the unique computer algebra system offering automatic case discussion and recombination.