Gaul (Latin: Gallia) was a region of Western Europe during the Iron Age that was inhabited by Celtic tribes, encompassing present day France, Luxembourg, Belgium, most of Switzerland, Northern Italy, as well as the parts of the Netherlands and Germany on the west bank of the Rhine. It covered an area of . According to the testimony of Julius Caesar, Gaul was divided into three parts: Gallia Celtica, Belgica and Aquitania. Archaeologically, the Gauls were bearers of the La Tène culture, which extended across all of Gaul, as well as east to Raetia, Noricum, Pannonia and southwestern Germania during the 5th to 1st centuries BC. During the 2nd and 1st centuries BC, Gaul fell under Roman rule: Gallia Cisalpina was conquered in 203 BC and Gallia Narbonensis in 123 BC. Gaul was invaded after 120 BC by the Cimbri and the Teutons, who were in turn defeated by the Romans by 103 BC. Julius Caesar finally subdued the remaining parts of Gaul in his campaigns of 58 to 51 BC. 

Roman control of Gaul lasted for five centuries, until the last Roman rump state, the Domain of Soissons, fell to the Franks in AD 486. While the Celtic Gauls had lost their original identities and language during Late Antiquity, becoming amalgamated into a Gallo-Roman culture, "Gallia" remained the conventional name of the territory throughout the Early Middle Ages, until it acquired a new identity as the Capetian Kingdom of France in the high medieval period. "Gallia" remains a name of France in modern Greek (Γαλλία) and modern Latin (besides the alternatives "Francia" and "Francogallia").
when did Caesar complete his conquest?
Julius Caesar finally subdued the remaining parts of Gaul in his campaigns of 58 to 51 BC. 
