This book was the first grammar of Anglo-Saxon, or Old English, to be published in English. Apparently aimed at increasing interest in Old English beyond academic environments, it is simple to understand and covers the basics of the language. It is principally based upon the extensive Old English grammars of George Hickes and Edward Thwaites, both of which were published in Latin, as was usual for dictionaries and grammars in the early eighteenth century.

Elizabeth Elstob was born in Newcastle upon Tyne in 1683 but following the death of her parents, she was educated at Canterbury by an uncle who disdained female education. Despite this, he eventually relented and allowed Elstob to study modern and ancient languages including Latin and French. By the 1690s she was living in Oxford where her brother, William, managed to introduce her to a group of scholars known as the Oxford Saxonians. The Saxonians sought to promote the study of England's Anglo-Saxon past in the face of indifference from other scholars of the time. In 1702, Elstob moved to London and spent much of the time studying Old English, publishing a translation of the life of Pope Gregory the Great by the Anglo-Saxon writer Ælfric in 1709. That volume was followed by this grammar in 1715. Both works were lavishly produced, the Rudiments being dedicated to Caroline of Ansbach, Princess of Wales (who was keen to encourage English arts and scholarship), and contained an engraved first initial which contained a small portrait of Elstob.

Soon after the publication of the grammar, William Elstob died, leaving Elizabeth with no source of income and mounting debts. She fled London, abandoning her possessions, including her books, and moved to Evesham in Worcestershire. At Evesham, she attempted to establish a girls' school, but that soon floundered. Little is known of her life until almost 20 years later, when she started working as governess to the Duke and Duchess of Portland. She died under their care in 1756.