Margravine Hedwig Sophie of Brandenburg
Hedwig Sophia of Brandenburg( 14 July 1623, Berlin- 26 June 1683, Schmalkalden) was Landgravine consort of Hesse- Kassel by marriage to William VI, Landgrave of Hesse- Kassel, and regent from 1663 until 1677 during the minority of her sons, William VII, Landgrave of Hesse- Kassel and Charles I, Landgrave of Hesse- Kassel.
Louis VIII, Landgrave of Hesse-Darmstadt
Louis VIII (German: "Ludwig") (5 April 1691 – 17 October 1768) was the Landgrave of Hesse-Darmstadt from 1739 to 1768.
He was the son of Ernest Louis, Landgrave of Hesse-Darmstadt and Margravine Dorothea Charlotte of Brandenburg-Ansbach.
Louis VI, Landgrave of Hesse-Darmstadt
Louis VI of Hesse-Darmstadt  (25 January 1630 – 24 April 1678) was Landgrave of Hesse-Darmstadt from 1661 to 1678.
He was the eldest of three sons of the Landgrave George II of Hesse-Darmstadt and Sophia Eleonore of Saxony.
Princess Caroline of Hesse-Darmstadt
Caroline of Hesse-Darmstadt (2 March 1746, Buchsweiler – 18 September 1821, Homburg) was Landgravine consort of Hesse-Homburg by marriage to Frederick V, Landgrave of Hesse-Homburg.
She was the eldest daughter of Louis IX, Landgrave of Hesse-Darmstadt and his wife Caroline.
She married Frederick V, Landgrave of Hesse-Homburg on 27 September 1768.
The marriage was contracted for diplomatic and political reasons as the symbol of an inheritance dispute between their respective families.
Caroline and Frederick V produced many children but their marriage never developed into a personal relationship, and they lived mostly separated lives.
Caroline often spent time in the famed little villa that was given to her use in the forest near Homburg.
Sophia Eleonore of Saxony
Sophia Eleonore of Saxony (23 November 1609 – 2 June 1671) was a duchess of Saxony by birth and the landgravine of Hesse-Darmstadt from 1627 to 1661 through her marriage to Landgrave George II.
She was the eldest surviving child of John George I, Elector of Saxony, and Magdalene Sibylle of Prussia.
William VI, Landgrave of Hesse-Kassel
William VI, Landgrave of Hesse- Kassel( 23 May 1629 – 16 July 1663), known as William the Just, was Landgrave of Hesse- Kassel from 1637 to 1663.
Philip, Landgrave of Hesse-Philippsthal
Philip of Hesse- Philippsthal( 14 December 1655 – 18 June 1721) was the son of William VI, Landgrave of Hesse- Kassel and Hedwig Sophia of Brandenburg.
He was the first landgrave of Hesse- Philippsthal from 1663 to 1721 and the founder of the fifth branch of the house of Hesse.
Landgravine Auguste of Hesse-Homburg
Landgravine" Auguste" Fredericka of Hesse- Homburg( full German name:" Auguste Friederike, Landgräfin von Hessen- Homburg"; 28 November 1776, Bad Homburg vor der Höhe, Landgraviate of Hesse- Homburg, Holy Roman Empire – 1 April 1871, Ludwigslust, Grand Duchy of Mecklenburg- Schwerin), was a member of the House of Hesse and a Landgravine of Hesse- Homburg by birth.
Through her marriage she was also a member of the House of Mecklenburg and Hereditary Grand Duchess of Mecklenburg- Schwerin.
She was the sixth child and fourth daughter of Frederick V, Landgrave of Hesse- Homburg and his wife Landgravine Caroline of Hesse- Darmstadt, in turn daughter of Louis IX, Landgrave of Hesse- Darmstadt.
Louis IX, Landgrave of Hesse-Darmstadt
Louis IX of Hesse- Darmstadt( 15 December 1719 – 6 April 1790) was the Landgrave of Hesse- Darmstadt from 1768- 1790.
He was a son of Louis VIII, Landgrave of Hesse- Darmstadt, and Charlotte of Hanau- Lichtenberg and Müntzenberg.
He was born in Darmstadt on 15 December 1719.
On 12 August 1741, Louis married Caroline of Zweibrücken, daughter of Christian III, Duke of Zweibrücken.
They had three sons and five daughters, including: In 1775, Louis married Marie Adelaide of Cheirouze, countess of Lemberg.
On 6 April 1790 Louis died in Pirmasens.
Louis V, Landgrave of Hesse-Darmstadt
Louis V of Hesse-Darmstadt (24 September 1577 – 27 July 1626) was the Landgrave of Hesse-Darmstadt from 1596 to 1626.
He was born on 24 September 1577 as the son of George I, Landgrave of Hesse-Darmstadt and Magdalene of Lippe.
In 1604 he inherited a part of Hessen-Marburg after the death of Louis IV of Hesse-Marburg who was childless.
The other half went to Maurice of Hesse-Kassel (or Hesse-Cassel), but since Maurice was a Calvinist, Ludwig claimed a right on the whole of Hesse-Marburg.
Lutheran professors of the University of Marburg who refused to convert to Calvinism founded in 1607 the University of Gießen which was named "Ludoviciana".
This led to a conflict during the Thirty Years' War, between Louis V, who stood on the side of the Emperor, and Maurice, who was on the side of the Protestants.
Hesse-Darmstadt suffered severely from the ravages from the Swedes during the conflict.
The Landgrave died in 1626 and he was succeeded by George II, Landgrave of Hesse-Darmstadt.
In 1722, Johann Georg Liebknecht, an astronomer at the University of Gießen, named a star, which he thought was a planet, Sidus Ludoviciana after Ludwig V.

Question: Who is Louis Vi, Landgrave Of Hesse-Darmstadt's maternal grandfather?
Answer: John George I, Elector of Saxony