Singular provides

- highly efficient core algorithms,
- a multitude of advanced algorithms in the above fields,
- an intuitive, C-like programming language,
- easy ways to make it user-extendible through libraries, and
- a comprehensive online manual and help function.

Its main computational objects are ideals, modules and matrices over a large number of baserings. These include

- polynomial rings over various ground fields and some rings (including the integers),
- localizations of the above,
- a general class of non-commutative algebras (including the exterior algebra and the Weyl algebra),
- quotient rings of the above,
- tensor products of the above.

- Gröbner resp. standard bases and free resolutions,
- polynomial factorization,
- resultants, characteristic sets, and numerical root finding.

Its advanced algorithms, contained in currently more than 90 libraries, address topics such as **absolute factorization**, **algebraic D-modules**, **classification of singularities**, **deformation theory**, **Gauss-Manin systems**, **Hamburger-Noether (Puiseux) development**, **invariant theory**, **(non-) commutative homological algebra, ** **normalization**, **primary decomposition**, **resolution of singularities**, and **sheaf cohomology**.

Further functionality is obtained by combining Singular with third-party software linked to SINGULAR. This includes tools for **convex geometry**, **tropical geometry**, and **visualization**.