The Wallis Collection contains books on mathematics and maths education and includes works by Robert Record (the man who introduced the = symbol), such as The grounde of artes: teaching the perfecte worke and practise of arithmetike (1582) and works by and about Isaac Newton, such as Newton's Principia in its first American edition (1846).

The books were formerly owned by Peter Wallis (1918-1992), a lecturer in the School of Education. There are almanacs, works on algebra and geometry, school text books, works on astronomy including J.F.W. Herschel's Astronomy (1835), guides to measuring, book-keeping, ready reckoners, treatises, Euclid's Elements and manuals.

The archive comprises mainly correspondence addressed to Sir Walter and his first wife Pauline Lady Trevelyan nee Paulina Jermyn. The letters reflect the couple's interests in natural history, botany, geology, antiquities, travel, temperance, phrenology, art and literature, and include examples from many well known contemporaries.

There is also material relating to the history of the Trevelyan family, accumulated during Walter and Charles Edward Trevelyan's preparation of 'The Trevelyan Papers' for publication.

The archive also features diaries and journals, sketchbooks, notes for speeches and scrapbooks. There is material relating to the North East of England, including proposed railways, Tyne crossings at Hexham and decoration of the Great Hall at Wallington.

The Ritchie Collection comprises books, pamphlets, atlases and charts relating to the history of Hydrography, the branch of marine science concerned with studying, surveying and mapping the earth's seas and waters. The collection represents the personal library of the former Hydrographer to the Royal Navy, Rear Admiral George Stephen Ritchie (b. 1914). Its contents reflect Rear Admiral Ritchie's professional achievements, as well as his personal interest in the history of Hydrography and surveying. Technical and cartographic material sits alongside numerous primary and secondary texts on the history of Hydrography, as well as publications on the broader themes of seafaring and exploration.

There are contemporary accounts, including The Surveying Voyage of HMS Flag by Captain R. N. Blackwood (1848) and An Account of the Natives of the Tonga Islands by William Mariner (1817), as well as more recent histories such as Vice Admiral Sir Archibald Day's The Admiralty Hydrographic Service 1795-1919 (1967). The great pioneers in the field, including James Cook and William Fitzwilliam Owen, are also represented. Many of the secondary texts in the collection are authors' signed copies and Rear Admiral Ritchie's own works are present, too, including Challenger: the Life of a Survey Ship (1957), a biography of the ship commanded by him on a celebrated voyage of 1951-1952.

Consists of papers relating to Professor Randell's professional and academic associations throughout his career.

The Merz Collection is the mathematical library of John Theodore Merz (1840-1922), an electrical engineer. Merz also had an interest in philosophy, and the collection also includes books amassed by him during the writing of his work The History of European Thought in the Nineteenth Century. These 4000 volumes are strongest in Mathematics and the History of European Thought, but also include notable works on science, European history and German Literature.A particular highlight is An investigation of the laws of thought: on which are founded the mathematical theories of logic and probabilities (1854) by George Boole, the English mathematician and philosopher, and inventor of Boolean logic, the basis of modern digital computer logic.The collection is also of interest for its book-bindings: mostly leather or half-leather bindings by Zaehnsdorf of London.

There are over 150 maps in Special Collections. In the main, they are pre-twentieth century and cover areas in north-eastern England.

This is a small collection of notebooks and photograph albums which belonged to John William Heslop Harrison (1881-1967), at one time Professor of Botany at Newcastle University. The notebooks contain notes on plant biology, pollination and plant genetics while the albums include photographs of Iraq, dated 1938-1941. The collection also includes Proceedings of the University of Durham Philosophical Society 1955-1956 in various stages of editing.

This is a small collection of papers, once belonging to Thomas Henry Havelock (1877-1968), Professor of Mathematics, Newcastle University.

This collection of illustrations by local artist Thomas Hair (c.1810-1875) depicts the mining industry and the coal trade in the North East in the nineteenth century. The illustrations are based on Hair's watercolours on the same topic. The illustrations in the collection highlight numerous aspects of the region's mining heritage, including collieries, machinery, and river trade scenes. Many of the illustrations also show the everyday workings of the industry and those involved in it.

This collection of early works on agriculture is rich in eighteenth and nineteenth-century reports on farming in many parts of Great Britain. The collection had as its nucleus the historical library of the late Professor D.A. Gilchrist (d. 1927), who held the Chair of Agriculture in Armstrong College from 1902 to 1927.

A collection highlight is William Billington's A series of facts, hints, observations, and experiments on the different modes of raising young plantations of oaks (1825) which demonstrates the common preoccupation of many early nineteenth-century estate owners with growing trees which would be suitable for use in shipbuilding.