Yuki Kajiura (梶浦 由記 Kajiura Yuki) is the composer who created Puella Magi Madoka Magica's soundtrack. Kajiura founded Kalafina, the group that performed Madoka's ending song, Magia. She also performs under the name FictionJunction.
Kajiura makes heavy use of non-Japanese languages, including giving Latin titles to Madoka's songs. She frequently writes lyrics in "Kajiuraese" (also known as Kajiurago or Kajiuran), a made-up language which is designed to sound pleasing and inspired by romance languages.
See the Soundtrack page for details on her Madoka-related works.
Some examples of the anime soundtracks she has composed: My-HiME, My-Otome Zwei, Fist of the North Star True Saviour Legend, El Cazador de la Bruja, Tsubasa Tokyo Revelations, Tsubasa Shunraiki, Pandora Hearts, Fate/Zero and Sword Art Online