Both the Ars Antiqua and the Ars Nova are musical styles that belong to the Medieval period of Western music history.
Ars Antiqua (Latin for "old art") refers to the style of polyphonic music that flourished in Europe from roughly 1170 to 1310. It is associated with the Notre Dame school of composers, including Leonin and Perotin, and features organum, conductus, and early motet forms.
Ars Nova ("new art") followed from about 1310 to 1377 and was named after Philippe de Vitry's treatise. It introduced greater rhythmic complexity and new time signatures, expanding the possibilities of musical notation. Guillaume de Machaut was its most prominent composer.
Both movements predate the Renaissance, the Baroque, the Classical, and the Romantic periods. The Medieval period in music is generally dated from around 500 to 1400 CE, and both Ars Antiqua and Ars Nova fall squarely within this timeframe.