Alexander Courage (born December 10, 1919) is a 20th century American composer of music, primarily for television and motion pictures.

He is probably best known for writing the theme music to the original Star Trek television series. Words (not the ones sung by Bill Murray as a lounge singer in a famous Saturday Night Live sketch) were written for that theme by Star Trek creator Gene Roddenberry, not because Roddenberry ever expected the words to be sung, but because by claiming acknowledgement as the co-writer he earned half of the royalties from the song.