Give Me Your Hand

"Give Me Your Hand" (Irish: "Tabhair dom do Lámh") is a tune from early 17th century Ireland by Rory Dall O'Cahan. It is one of the most widely recorded pieces of Irish traditional music.
Composer.
According to Edward Bunting, in The Ancient Music of Ireland, this harp tune was written in about 1603 by Rory Dall O'Cahan.
This tune, revived by Seán Ó Riada, was originally a composition of the blind Derry harpist Ruaidri Dáll Ó Catháin. He wrote it while (in) Scotland, where he had a disagreement with a Lady Eglington. He composed the tune for her when she apologized. from the Wolfetones.
Captain Francis O'Neill suggests
Proud and spirited, he resented anything in the nature of trespass on his dignity. Among his visits to the houses of Scottish nobility, he is said to have called at Eglinton Castle, Ayrshire. Knowing he was a harper, but being unaware of his rank, Lady Eglinton commanded him to play a tune. Taking oftence at her peremptory manner, Ó Catháin refused and left the castle. When she found out who her guest was her ladyship sought and effected a speedy reconciliation. This incident furnished a theme for one of the harper’s best compositions. “Tabhair Damh do Lámh,” or “Give Me Your Hand!” The name has been latinized into “Da Mihi Manum.”
The fame of the composition and the occasion which gave birth to it reaching the ear of King James the Sixth, induced him to send for the composer. Ó Catháin accordingly attended at the Scottish court, and created a sensation.
There are other stories and legends, but no authoritative evidence or references are known.
The tune is sometimes claimed to be written by the famous harpist [O'Carolan], who lived some years later. However, there is no reference in the Bunting collection of O Carolan’s music. Nor should Rory Dall O'Cahan be confused with another blind poet at around the same time, Rory 'Dall' Morrison.
A number of apocryphal stories have circulated about the circumstances of the tune's composition; further details can be seen at Andrew Kuntz's The Fiddler's Companion.
Later references to the tune.
The Fiddler's Companion says
 The Latin title first appears in the Wemyss manuscript of 1644 and in the Balcarres manuscript of 1692 and then
 The melody's popularity was long-lived, as attested by its appearance in many collections throughout the 18th century, including Wright's Aria di Camera (1730), Neal's Celebrated Irish Tunes (c. 1742—a revised date from the oft-given 1721 or 1726, this based on watermark research—see the appendix to the 2001 edition of O’Sullivan’s Carolan), Burk Thumoth's Twelve English and Irish Airs (c. 1745-50), Thompson's Hibernian Muse (c. 1786), Brysson's Curious Selection of Favourite Tunes (c. 1790), and Mulholland's Ancient Irish Airs (1810). 
English and Irish titles first seem to have appeared in 'A Collection of Ancient Irish Airs', by John Mulholland, 2 vols. Belfast, 1810.
Seán Ó Riada is attributed with reviving the tune in the late 1960s. The Wolfetones also contributed to the tune's development by adding words of reconciliation at a time of violence in Northern Ireland during The Troubles.
Some recordings of "Give Me Your Hand" (Tabhair dom do Lámh).
The Wolfe Tones and Family Pride are the only known recordings with vocals.