“A.B.” is an abbreviation that can mean different things depending on context:

• Artium Baccalaureus (A.B.) — the Latin name for a Bachelor of Arts (B.A.) degree, used by some universities (especially older or traditional ones).
• Abbreviation of names:
  • Example: A. B. Smith = initials for a person’s first and middle names.

In short, A.B. most commonly refers to a Bachelor of Arts degree in Latin form, or just initials in a name.