This is not an exhaustive list of books but will provide a good general introduction.
Anglo-Saxon England, Sir Frank Stenton. The essential reference book.
The Beginnings of English Society, Dorothy Whitelock. Essential reading.
The Anglo-Saxons, (ed) James Campbell. An introduction to the history of Anglo-Saxon England covering political, religious, cultural, social, legal and economic matters with reference to source material and with photographs and illustrations.
In Search of the Dark Ages, Michael Wood. An introduction to Sutton Hoo, Offa, Alfred the Great, Æthelstan, Eric Bloodaxe, and Æthelred the Unready.
The Wiley Blackwell Encyclopedia of Anglo-Saxon England, (ed) Michael Lapidge et al. A general reference book with numerous articles by experts on a range of topics. This may be best accessed via a reference library as it is rather more expensive than most of the books on this list.
Daily Life in Anglo-Saxon England, Sally Crawford. A discussion of the daily lives of ordinary men, women and children in Anglo-Saxon England. The book’s topics cover: The Anglo-Saxons in England; society, taxes and administration; housing and households; population density and life expectancy; food and drink; clothing and appearance; trade and travel; death and religion; health, sickness and survival; slaves, criminals and outcasts; and conquest and conclusions.
The Year 1000. An Englishman’s Year, Robert Lacy and Danny Danziger. An insight into the daily life of ordinary men and women in the year 1000 month by month with illustrations taken from the “Labour of the Months” the Julius calendar produced at Canterbury in Kent.
Original texts and literature
A History of the English Church & People, Bede (various editions and translations available, but Michael Swanton’s is very good). Bede “set himself to examine all available records, to secure verbal or written accounts from reliable living authorities, to record local traditions and stories, to interpret significant events, and, in short, to compile as complete and continuous a history of the English Church and people as lay within his power.” The views and records of this Anglo-Saxon writer should not be too easily dismissed.
Byrhtferth’s Manual (A.D. 1011), (ed) S.J.Crawford. This is an 11th century work by a great scholar on rhetorical and grammatical subjects, a table of weights and measures, and three theological tracts.
The Anglo-Saxon World, an Anthology, (ed) Kevin Crossley- Holland. A collection of Old English texts-chronicles, laws, letters, charters, charms and poems – translated into modern English with an introduction.
A Choice of Anglo-Saxon Verse, (ed) Richard Hamer. Examples of Anglo-Saxon verse – The Battle of Maldon, The Dream of the Rood, The Wanderer, The Seafarer etc. – in Old English with parallel modern English translation.
Runic and Heroic Poems of the Old Teutonic Peoples, (ed) Bruce Dickins. Includes Runic Poems, Waldhere, Finn, Deor and Hildebrand.
Archaeology and material culture
1066. The Hidden History of the Bayeux Tapestry, Andrew Bridgford. Despite its superficial Norman viewpoint, the author reveals some of the hidden meaning of the Tapestry recording a very different story from the English viewpoint.
Anglo-Saxon Pottery and the Settlement of England, J.N.L.Myres. One of the most important books on a much-neglected subject.
Anglo-Saxon Crafts, Kevin Leahy. This book discusses the skills and techniques involved in creating the treasures of the Anglo-Saxons.
Anglo-Saxon Art, Leslie Webster. A discussion of Anglo-Saxon art in its wider cultural context, showing how it was shaped, transformed and given meaning.
Anglo-Saxon Animal Art and its Germanic Background George Speake. Anglo-Saxon Art of the 6th and 7th centuries. Mainly ‘the decoration of personal jewellery, belt-fittings, brooches, pendants, weapons,’ drinking horns etc.
Dress in Anglo-Saxon England, Gale Owen-Crocker. An encyclopedic study of Anglo-Saxon dress, from the 5th to 11th centuries based on evidence from archaeology, texts and art.
The Mead-Hall, Stephen Pollington. The Mead-Hall was the centre of early English culture.
Old English language
First Steps in Old English Stephen Pollington. This “teach-yourself” book covers the essentials of vocabulary and grammar and has achieved something like classic status.
A Concise Anglo-Saxon Dictionary, J.R. Clark Hall. This provides Old English to Modern English vocabulary.
Wordcraft: New English to Old English Dictionary and Thesaurus. Stephen Pollington. The book provides a basic introduction to the vocabulary of Modern English into Old English aimed at those who wish to compose original work in Old English.