thumb|right|Henry Savile in 1621. School of [[Marcus Gheeraerts the Younger]]
Sir Henry Savile (30 November 154919 February 1622) was an English scholar and mathematician, Warden of Merton College, Oxford, and Provost of Eton. He endowed the Savilian chairs of Astronomy and of Geometry at Oxford University, and was one of the scholars who translated the New Testament from Greek into English. He was a Member of the Parliament of England for Bossiney in Cornwall in 1589, and Dunwich in Suffolk in 1593. He established a reputation as a Greek scholar and mathematician by voluntary lectures on Ptolemy's Almagest, and in 1575 became Junior Proctor of the university. In 1578 he travelled on the continent of Europe, where he collected manuscripts, and is said to have been employed by Queen Elizabeth as her resident in the Low Countries. On his return he was named Greek tutor to the Queen. In 1585 he was established as Warden of Merton by a vigorous exercise of the interest of Burghley and Secretary Walsingham. He proved a successful and autocratic head of house, generally unpopular with Fellows and undergraduates, but under him the college flourished. His translation of four books of the Histories of Tacitus, with the learned Commentary on Roman Warfare (1591), enhanced his reputation. He also sat in Parliament as one of the two members for Bossiney in 1589 and for Dunwich (both were notorious rotten boroughs) in 1593.
On 26 May 1596 he obtained the provostship of Eton College, the reward of persistent begging. He was not qualified for the post under the statutes of the college, for he was not in holy orders, and the Queen was reluctant to name him. Savile insisted with considerable ingenuity that the Queen had a right to dispense with statutes, and at last he got his way. In February 1601 he was put under arrest on suspicion of having been concerned in the rebellion of the Earl of Essex.
His edition of the works of St. John Chrysostom in eight folio volumes was published in 1610–1613. It was printed by the king's printer on a private press erected at the expense of Sir Henry, who imported the type. The Chrysostom cost him £8,000 and did not sell well. However, it was the most considerable work of pure learning undertaken in England in his time,
Savile was keen to impart his understanding of mathematics to his students at Oxford, and in founding the Geometry chair he gave thirteen preparatory lectures on the original books of Euclid's Elements in 1620. These were published in 1621 as his Praelectiones tresdecim in principium elementorum Euclidis, Oxonii habitae MCDXX. Oxonii: Excudebant Iohannes Lichfield, & Iacobus Short, 1621. ('Thirteen introductory lectures on the beginning of the Elements of Euclid, held at Oxford in 1620'.) It was Savile who first traced the hand of Theon of Alexandria as a commentator on Euclid, and Savile who first clearly distinguished Euclid of Alexandria from Euclid of Megara (an earlier philosopher), until then largely conflated with each other in medieval and Renaissance scholarship.
The edition published in England, until then the only one containing all the extant works attributed to Euclid, was that of Dr David Gregory, published at Oxford in 1703, with the title, Εὐκλείδου τὰ σωζόμενα, Euclidis quae supersunt omnia. The parallel Greek text is that of the 1533 Basel edition by Simon Grynäus, corrected from Savile's 13th century Greek MSS. which Savile bequeathed to the Savilian Library, and from Savile's annotations in his own copy. The Latin translation, which accompanies the Greek on the same page, is for the most part that of Commandino. It was a collection of mathematical works, including the related subjects of optics, harmonics, mechanics, cosmography, the applied sciences of surveying, navigation, and fortification, and a quantity of fine printed books, primarily from the 16th century. Dr. John Wallis (Savilian professor, 1649-1704) gave the Savilian library 'the largest of its accretions', and many more were provided after his death in 1703. In the eighteenth century, not much more was added to Savile's collection, but later Stephen Rigaud (Geometry Chair, 1810–27; Astronomy, 1827–39)
In 1835 Savile's library was moved to the south-east corner of the Bodleian quadrangle, where it remained until 1884, when the Savilian professors agreed to hand over its administration to the Bodleian Library.
His brother, Thomas Savile (died 1593), was also a member of Merton College and had some reputation as a scholar.