| Name | Description | Type | Package | Framework |
| AbelianGroup | This interface defines an abelian group. | Interface | org.jscience.mathematics.algebraic.groups | JScience |
| AbelianGroup .Member | This interface defines a member of an abelian group. | Interface | org.jscience.mathematics.algebraic.groups | JScience |
| CyclicGroup | The CyclicGroup class represents the nth cyclic group. | Class | org.jscience.mathematics.algebraic.groups | JScience |
| DihedralGroup | The DihedralGroup class represents the nth dihedral group. | Class | org.jscience.mathematics.algebraic.groups | JScience |
| FiniteGroup | Superclass for finite groups. | Class | org.jscience.mathematics.algebraic.groups | JScience |
| Group | This interface defines a group. | Interface | org.jscience.mathematics.algebraic.groups | JScience |
| Group .Member | This interface defines a member of a group. | Interface | org.jscience.mathematics.algebraic.groups | JScience |
| LieGroup | The LieGroup class provides an encapsulation for Lie groups. | Class | org.jscience.mathematics.algebraic.groups | JScience |
| Loop | This interface defines a loop (a quasigroup with an identity element). | Interface | org.jscience.mathematics.algebraic.groups | JScience |
| Loop .Member | Interface | org.jscience.mathematics.algebraic.groups | JScience | |
| Magma | Interface | org.jscience.mathematics.algebraic.groups | JScience | |
| Magma .Member | This interface defines a member of a magma. | Interface | org.jscience.mathematics.algebraic.groups | JScience |
| Monoid | This interface defines a monoid (a semigroup with an identity element). | Interface | org.jscience.mathematics.algebraic.groups | JScience |
| Monoid .Member | Interface | org.jscience.mathematics.algebraic.groups | JScience | |
| OrderedGroup | This interface defines an ordered group. | Interface | org.jscience.mathematics.algebraic.groups | JScience |
| Quasigroup | This interface defines a quasigroup (a magma in which division is always possible, not necessarily associative). | Interface | org.jscience.mathematics.algebraic.groups | JScience |
| Quasigroup .Member | Interface | org.jscience.mathematics.algebraic.groups | JScience | |
| QuaternionGroup | The QuaternionGroup class represents the quaternion group. | Class | org.jscience.mathematics.algebraic.groups | JScience |
| Semigroup | Interface | org.jscience.mathematics.algebraic.groups | JScience | |
| Semigroup .Member | Interface | org.jscience.mathematics.algebraic.groups | JScience | |
| U1 | The U1 class provides an encapsulation for U(1) groups. | Class | org.jscience.mathematics.algebraic.groups | JScience |