The term normal has many meanings:

• In behavior etc.: normal means not deviating very much from the average; 'not normal' is often used in a negative sense (improper, sick, etc.). Abnormality varies greatly in how pleasant or unpleasant this is for other people; somebody may half-jokingly be called 'pleasantly disturbed'. See also mainstream, temperance, vanilla sex, equilibrium, stability, reality, peace, health, middle way, and on the other hand eccentricity, perversion, paraphilia, intersexual, disease, disability, mental illness, addiction, war, crime, fantasy, dream, hallucination, illusion. Some terms could fit in both lists, for example boredom: too much "normality" can be boring, but boredom is a kind of suffering, which can be considered "not normal".

• In education, a normal school is a school in which teachers are trained.

• In chemistry, the normality of an acid or an alkali is one way to measure its concentration.

• In geometry and physics: a normal is a line perpendicular to a surface.
• In statistics, a normal variable is a random variable that follows the normal distribution.
• In abstract algebra (in particular, group theory): a normal subgroup is a subgroup that is invariant under conjugation.
• In linear algebra: a normal matrix is a matrix which commutes with its conjugate transpose.
• In functional analysis: a normal operator is a linear operator on a Hilbert space that commutes with its adjoint.
• In abstract algebra: a normal extension is a field extension in which certain polynomials can be completely factored into linear polynomials.
• In topology: a normal space is a topological space in which disjoint closed sets can be separated by neighborhoods.
• In mathematical analysis: a normal number is a number whose digit sequence is random.
• In set theory: a normal function is a continuous strictly increasing function from ordinals to ordinals.
• In category theory: a normal morphism is a morphism that arises as the kernel or cokernel of some other morphisms.