John Annesley, 4th Earl of Anglesey
John Annesley, 4th Earl of Anglesey( 18 January 1676 – 18 September 1710), was an English peer and landowner.
A younger son of James Annesley, 2nd Earl of Anglesey( 1645 – 1690), by his marriage to Lady Elizabeth Manners, daughter of John Manners, 8th Earl of Rutland, he succeeded to the family estates and Earldom of Anglesey on the death of his brother James in 1701/ 02.
On 21 May 1706 he married Lady Henrietta Maria Stanley( 1687 – 1718), the daughter of William Stanley, 9th Earl of Derby.
Some years later, the title of Baron Strange was called out of abeyance in her favour and she became Baroness Strange in her own right.
In 1710, shortly before his death, Anglesey was appointed as Vice Treasurer, Receiver- General and Paymaster of the Forces for Ireland and was sworn into the Queen's Privy Council.
James FitzGerald, 6th Earl of Desmond
James FitzGerald, 6th Earl of Desmond( d. 1462), called' the Usurper', was the youngest son of Gerald FitzGerald, 3rd Earl of Desmond, and Lady Eleanor, daughter of James Butler, 2nd Earl of Ormond.
Elizabeth Annesley, Countess of Anglesey (died 1700)
Elizabeth Annesley, Countess of Anglesey( died 7 December 1700), formerly Lady Elizabeth Manners, was the wife of James Annesley, 2nd Earl of Anglesey, and the mother of the 3rd, 4th and 5th Earls.
Elizabeth was a daughter of John Manners, 8th Earl of Rutland, and his wife, the former Frances Montagu.
Her sisters, Margaret, Frances and Dorothy, all became countesses, while another, Anne, became a Viscountess.
Elizabeth Manners married the future Earl of Anglesey on 17 September 1669( or 1666), and they had four children: James Annesley inherited his father's earldom on 6 April 1686.
He died four years later, at which point Elizabeth became Dowager Countess.
The earl having died intestate, she was granted the administration of his estate in England and Ireland, with an estimated value of £ 4,000 per annum.
The countess was buried on 10 December 1700 at St. James's, Westminster.
Gilbert Talbot, 3rd Baron Talbot
Gilbert Talbot, 3rd Baron Talbot( c. 1332–1387) was an English nobleman and soldier.
He was the grandfather of John Talbot, 1st Earl of Shrewsbury.
James Annesley, 2nd Earl of Anglesey
James Annesley, 2nd Earl of Anglesey FRS (c. 1645 – 1 April 1690), styled Lord Annesley from 1661 to 1686, was a British peer.
He was the son of Arthur Annesley, 1st Earl of Anglesey and Elizabeth Altham.
He matriculated at Christ Church, Oxford University, on 4 December 1661.
He married Lady Elizabeth Manners, daughter of John Manners, 8th Earl of Rutland and Frances Montagu, on 17 September 1669.
They had children:
He died intestate and the administration of his estate in England and Ireland, with a value estimated at £4,000 per annum, was granted to his widow on 6 June 1690.
He was briefly a Whig member of parliament for County Waterford in 1666, after his brother-in-law, Richard Power succeeded in his father's (Irish) peerage.
He was elected to the English seat of Winchester in the parliaments of May and October 1679, and again in 1681.
He was a Justice of the Peace for Hampshire and Surrey (1674–81), colonel of the Hampshire militia (1675–81), Custos Rotulorum of Hampshire(1675–81) and a Deputy Lieutenant of Hampshire (1680–81).
On 6 April 1686 Annesley succeeded to his father's peerages of Baron Mountnorris and Earl of Anglesey, in Wales [E., 1661], Baron Annesley, of Newport Pagnel, Buckinghamshire [E., 1661] and Viscount Valentia.
Thomas Butler of Cahir
Thomas Butler of Cahir( 1448- 1476) was the grandson of James" Gallda" Butler who was the third son of James Butler, 3rd Earl of Ormond.
He was born and died in Cahir Castle, Tipperary, Ireland.
James Annesley, 3rd Earl of Anglesey
James Annesley, 3rd Earl of Anglesey (3 Jul 1674–21 January 1702), succeeded to his Earldom on the death of his father, James Annesley, 2nd Earl of Anglesey in 1690, the same year in which he matriculated at Christ Church, Oxford.
His mother was Lady Elizabeth Manners, daughter of John Manners, 8th Earl of Rutland.
In October 1699 he married Lady Catherine Darnley, illegitimate daughter of James II of England by Catherine Sedley, Countess of Dorchester.
They had a daughter, Lady Catherine Annesley, who married William Phipps and was ancestress of the Baron Mulgrave.
The couple were legally separated in June 1701, on the grounds of Anglesey's cruelty to his wife.
The earl, already suffering from consumption, died in the following January.
Thomas Butler, 10th Earl of Ormond
Thomas Butler, 10th Earl of Ormonde, 3rd Earl of Ossory, Viscount Thurles( c. 153122 November 1614), was an Irish peer and the son of James Butler, 9th Earl of Ormond and Lady Joan Fitzgerald daughter and heiress- general of James FitzGerald, 10th Earl of Desmond.
He was Lord Treasurer of Ireland and a very prominent personage during the latter part of the 16th century.
Ralph Neville, 3rd Earl of Westmorland
Ralph Neville, 3rd Earl of Westmorland( c. 1456 – 6 February 1499) was an English peer.
He was the grandfather of Ralph Neville, 4th Earl of Westmorland.
James Annesley
James Annesley( 1715–5 Jan 1760) was an Irishman with a claim to the title Earl of Anglesey, one of the wealthiest estates in Ireland.
The dispute between Annesley and his uncle Richard Annesley was infamous in its time, but his story is perhaps best known today as a possible inspiration for the 19th- century novel" Kidnapped" by Robert Louis Stevenson, among other works of literature.

Question: Who is James Annesley, 3Rd Earl Of Anglesey's paternal grandfather?
Answer: Arthur Annesley, 1st Earl of Anglesey