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• Natural numbers (${\displaystyle \mathbb {N} }$)
• Integers (${\displaystyle \mathbb {Z} }$)
• Rational numbers (${\displaystyle \mathbb {Q} }$)
• Constructible numbers
• Algebraic numbers (${\displaystyle \mathbb {A} }$)
• Closed-form numbers
• Periods (${\displaystyle {\mathcal {P}}}$)
• Computable numbers
• Arithmetical numbers
• Set-theoretically definable numbers
• Gaussian integers
  • Gaussian rationals
• Eisenstein integers

• Division algebras: Real numbers (${\displaystyle \mathbb {R} }$)
• Complex numbers (${\displaystyle \mathbb {C} }$)
• Quaternions (${\displaystyle \mathbb {H} }$)
• Octonions (${\displaystyle \mathbb {O} }$)

• Over ${\displaystyle \mathbb {R} }$:
• Split-complex numbers
• Split-quaternions
• Split-octonions
  Over ${\displaystyle \mathbb {C} }$:
• Bicomplex numbers
• Biquaternions
• Bioctonions

• Dual numbers
• Dual quaternions
• Dual-complex numbers
• Hyperbolic quaternions
• Sedenions  (${\displaystyle \mathbb {S} }$)
• Trigintaduonions  (${\displaystyle \mathbb {T} }$)
• Split-biquaternions
• Multicomplex numbers
• Geometric algebra/Clifford algebra
  • Algebra of physical space
  • Spacetime algebra
  • Plane-based geometric algebra

• Cardinal numbers
• Extended natural numbers
• Extended real numbers
  • Projective
• Extended complex numbers
• Hyperreal numbers
• Levi-Civita field
• Ordinal numbers
• Supernatural numbers
• Surreal numbers
• Superreal numbers

• Irrational numbers
• Fuzzy numbers
• Transcendental numbers
• p-adic numbers (p-adic solenoids)
• Profinite integers
• Normal numbers

• Classification
• List