Thalia - Muse of comedy and idyllic poetry.  She is usually shown holding a comic mask, a shepherd's crook, and a wreath of ivy.
Melpomene [mel-po-men-ee] - Muse of tragedy.  She is  usually shown holding a tragic mask, the club of Hercules, and a wreath or vine leaves.
Cleo - Muse of history.
Euterpe - Muse of lyric poetry.
Terpsichore - Muse of music and dancing.
Erato - Muse of erotic poetry.
Calliope - Muse of epic poetry and rhetoric.
Urania - Muse of astronomy.
Polyhymnia or Polymnia - Muse of sacred hymns and harmony.