A symmetric space is, in differential geometry and representation theory, a smooth manifold whose group of symmetries contains an "inversion symmetry" about every point. Examples include:

• Riemannian symmetric space
• Hermitian symmetric space
• Quaternion-Kähler symmetric space
• Weakly symmetric space

In topology, symmetric space may also refer to:

• R₀ space, a topological space in which two topologically distinguishable points can be separated

In computational complexity theory, symmetric space may refer to undirected or reversible analogues of nondeterministic space complexity, for instance:

• SL (complexity), the class of problems solvable in logarithmic symmetric space