Sources

1) Source: English Baronies: a Study of Their Origin and Descent, 1086-1327. Reference: Page 6; Barony of Gloucester (Questionable reliability of evidence)
2) Source: The Henry Project . External Link
https://fasg.org/projects/henryproject/data/henry001.htm. Reference: Henry I (Questionable reliability of evidence)
3) Source: Chippenham & Stanleigh Deeds "Maud the Empress, daughter of King Henry [I] and Henry her son, Duke of Normandy"Dated: Probably 1151 Evidence for Matilda being Henry's daughter. External Link
http://discovery.nationalarchives.gov.uk/details/r/9071ca5f-ff22-495e-b2f7-9135696a0eec. Reference: 1213/1 (Data from direct source)
4) Source: Chronica Magistri Rogeri de Houdene "after whose death [Stephen] Henry, the son of Geoffrey, earl of Anjou, and of Matilda, the former empress of the Romans, and daughter of the before-named king Henry the First, took the helm of the kingdom of England" (Data from direct source)
5) Source: The Ecclesiastical History of England and Normandy: Volume III "when Prince Henry ascended the throne of England, he married Matilda, by whom he had William the Etheling, and Matilda the empress" (Data from secondary evidence)
6) Source: The Ecclesiastical History of England and Normandy: Volume III "This king, four months after he succeeded to the throne, disdaining to abandon himself to illicit connections, and be like horse and mule which have no understanding, married with royal pomp Matilda, a noble lady, by whom he had two children, Matilda and William." (Data from secondary evidence)
7) Source: The Ecclesiastical History of England and Normandy: Volume III "At the same time he married another daughter to Rotro count of Mortain, who bore her husband a daughter named Philippa." (Data from secondary evidence)
8) Source: Orderici Vitalis Historiæ Ecclesiasticæ Within a year of her coronation, Matilda bore a son called Henry: "Anno ab incarnatione Domini MLXVIII... priusquam annus perficeretur, filium nomine Henricum peperit.". Reference: Book 4 (Data from secondary evidence)
9) Source: The Henry Project . External Link
https://fasg.org/projects/henryproject/data/matil001.htm. Reference: Eadgyth/Matilda of Scotland
10) Source: The Ecclesiastical History of England and Normandy: Volume IV "King Henry, having lost his wife and his son, resolved after consulting his council, to contract another marriage, and having selected Adelaide, the beautiful daughter of the duke of Louvain, the marriage was celebrated"
11) Source: Chronica de gestis consulum Andegavorum "In the same year [1186], our lord the king of England gave Ermengard, his kinswoman, daughter of Richard, viscount de Beaumont, in marriage to William, king of Scotland" (Data from secondary evidence)
12) Source: Duchy of Lancaster: Deeds, Series L "Charter by Ralph (de Gernons], Earl of Chester, addressed to his Bishop of Bangor, etc., notifying that Robert, Earl of Gloucester, gave to Matilda his daughter, Countess of Chester" Evidence for Robert being father of Matilda. External Link
http://discovery.nationalarchives.gov.uk/details/r/C5685124. Reference: DL 25/36 (Data from direct source)
13) Source: Chronica Magistri Rogeri de Houdene "In the same year, William, earl of Gloucester, son of earl Robert, brother of the empress, gave his daughter in marriage to John, the son of the king of England, together with the earldom of Gloucester, in case he should be able to marry the said damsel with the sanction of our lord the pope. In return for this grant, the king of England, the father, gave to the elder daughters of the said earl two hundred pounds of yearly revenues in England, namely, to the wife of Amaurus, earl of Evreux, one hundred pounds, and to the wife of Richard, earl of Clare, one hundred pounds." (Data from direct source)