Complex sentence: Greek art (or, more correctly, art in Greece) began in the Cycladic and Minoan civilization, and gave birth to Western classical art in the subsequent Geometric, Archaic and Classical periods (with further developments during the Hellenistic Period).
Split into simpler sentences: Greek art (or, more correctly, art in Greece) began in the Cycladic and Minoan civilization. Minoan prehistorical civilizations, and gave birth to Western classical art in the subsequent Geometric, Archaic and Classical periods (with further developments during the Hellenistic Period).