Short answers, pulled from the story.
Habsburg rule of the Low Countries began in 1482 with the accession of Philip the Handsome, who inherited the territories from his mother Mary of Burgundy. It ended in 1581 for the northern provinces when the Seven United Provinces declared independence, and in 1797 for the southern provinces when Austria relinquished its claim through the Treaty of Campo Formio.
Philip II of Spain's despotism and Catholic persecutions sparked the Dutch Revolt and the Eighty Years' War. The northern provinces formed the Protestant Union of Utrecht in 1579 and declared independence as the Seven United Provinces through the Act of Abjuration in 1581. The southern provinces remained under Habsburg control.
The Seventeen Provinces were the territories of the Low Countries reorganised under Charles V. The Pragmatic Sanction of 1549 formally established them as a single entity held by one prince. They included regions such as Flanders, Brabant, Holland, Zeeland, Hainaut, Namur, Luxembourg, and Limburg.
The Spanish Habsburg line ended with the death of the childless Charles II in 1700. Following the War of the Spanish Succession from 1700 to 1714, the southern provinces passed to the Austrian Habsburgs under the Treaty of Rastatt and became known as the Austrian Netherlands.
Charles V was born in Ghent and succeeded his father Philip the Handsome as Duke of the Netherlands in 1506 at the age of six. He became King of Spain in 1516 and Holy Roman Emperor in 1519. Through the Pragmatic Sanction of 1549, he formally organised the Seventeen Provinces as a single political entity.
Austrian Netherlands was invaded by Revolutionary France and annexed following the Battle of Sprimont in 1794. The Peace of Basel in 1795 formalised the annexation. Austria formally relinquished its claim in 1797 through the Treaty of Campo Formio.