1. Angry; resentful, infuriated: Her haughtiness makes her father mad.
2. Suffering from a disorder of the mind; insane, deranged: Van Gogh is reported to have had periods during which he was completely mad.
3. Marked or described as temporarily experiencing violent emotions, ideas, or behavior: Susanne was mad with jealousy when she saw her boyfriend talking with another girl.
4. Lacking restraint or reason; foolish: Jerome was mad to have hired both of those guys.
5. Foolish, impassioned, or demonstrating a strong attraction to someone or something: Ben's daughter was mad about sports.
6. Marked by extreme excitement, confusion, or agitation: There was a mad scramble for the tickets to the Olympic games.
7. Descriptive of something as amusing, a great deal of fun, hilarious: Dina and Fay had a mad time at the birthday party last night.
8. Affected by rabies; rabid: The neighbors could hear the mad dog howling because of the rabies that it was afflicted with.

For decades, language purists have been telling people that mad refers only to "insanity" and that we should not use it to mean "angry".

Regardless, mad does mean "angry", and expressions; such as, "I'm mad at him" and "She's mad because she wasn't invited to the party" are considered acceptable usages; although using such terms in formal writing might be considered "too informal and less desirable" than using "angry".

9. Etymology: the origin of mad is the shortened form of Old English gemad, "insane".