Here is a small, UK-biased selection of books, and a few important articles from academic journals. If you want to pursue anything further, these will lead you to hundred of other publications.

Books on the invention of the Celts

Simon James, 1999, The Atlantic Celts: Ancient people or modern invention? British Musem Press, London, & University of Wisconsin Press, Madison

My own book, directly examines the origins of the idea that some modern people in Ireland and Britain are Celts.  It is now out of print, but copies are usually available from the invaluable abebooks.com.

John Collis, 2003, The Celts: Origins, Myths and Inventions, Tempus, Stroud

John Collis's recent book considers the continental Iron Age peoples as well as the islanders, and outlines in great detail the intricacies of the development of notions about the Celts in modern archaeological scholarship. It is aimed more at the academic community, but is an important book for anyone interested in the subject.

Michael A Morse, 2005, How the Celts Came to Britain: Druids, Ancient Skulls and the Birth of Archaeology, Tempus, Stroud

Malcolm Chapman, 1992, The Celts; the construction of a myth, St. Martin's Press, London and New York

If you are interested in how the idea of Celts in the British Isles originated and developed, this  controversial and polemical book is nevertheless very useful.

How traditions get invented...

E. Hobsbawm and T. Ranger (eds.), The Invention of Tradition, Cambridge University Press 1983.

Contains papers on the invention of the romantic motif of the Scots Highlander, and for balance, the creation of many English 'traditions', during the nineteenth century.

Books on past identities in general

Paul Graves-Brown, Sian Jones and Clive Gamble (eds), Cultural Identity and Archaeology: The construction of European communities, Routledge, London and New York 1996

A valuable addition to the debate, containing general papers on the nature and construction of identities, past and present, plus several contributions specifically on the Celts. See specially the contributions by Renfrew, Collis and Fitzpatrick.
 

Siân Jones The archaeology of ethnicity : constructing identities in the past and the present, London : Routledge, 1997 

A major study of how we think about ethnicity, and how we can find evidence for it in the past; also, how we often create it when it wasn't really there...

General books on the Ancient Celts

Simon James, 1993, Exploring the World of the Celts, Thames & Hudson, London & New York (now available in paperback)

My first book on Celtic issues, a general survey of the early Celtic peoples of Europe, according to the traditional view. It was the reserach I undertook to write this book that first made me really question the whole idea of 'Ancient Celts', especially in the islands.

Conceived from a fairly traditional viewpoint, this contains a large collection of authoratitive papers on all aspects of Celtic life and culture.

V. Kruta, O. Frey, B. Raftery and M. Szabo, (eds.), 1991, The Celts, Thames & Hudson, London/Rizzoli and New York,

An enormous volume, comprising the catalogue of the 1991 Venice exhibition on the Celts, with a collection of thematic essays by almost everyone who is anyone in the field of Ancient Celtic studies. Lots of excellent colour illustrations, butbe warned, the English translations of some of the papers are very odd!

The academic debate on the meaning of 'Celticness'

• J.V.S. Megaw & M.R. Megaw, 'Ancient Celts and modern ethnicity', Antiquity, 70, No. 267, 1996, pp.175-81.

In this article Ruth and Vincent Megaw present a broadside against the 'Celt-scepticism' of people like Chapman, Hill, and Merriman. It accuses such scholars, very unfairly and quite implausibly in my view, of being motivated by English nationalism and anxiety rooted in the decline of British imperial power and the 'threat' of European federalism.

I was moved to write a response, arguing that the rejection of a Celtic past was partly due to more and better archaeological evidence making the idea hard to sustain, but also that such archaeologists are indeed ideologically motivated - but usually by a post-colonial and multi-cultural agenda, certainly not a nationalist one: that, ironically, their emphasis on multiple, diverse societies in Iron Age Britain, at least, and rejection of uniform Celts, recognises that Britain has always been home to multiple identities, peoples, or nations - as the new Scottish parliament, and Welsh assembly, re-emphasise in our own time. My response was:

• Simon James, 'Celts, politics and motivation in archaeology', Antiquity 72, 1998, No. 275, pp. 200-209

The Megaws subsequently produced a brief response to me and to others:

• 'The mechanism of (Celtic) dreams?': a partial response to our critics' Antiquity 72. No. 276 June 1998 (Page numbers not to hand)

Some  other papers on the Iron Age

• J.D. Hill, 'Can we recognise a different European past? A contrastive archaeology of later prehistoric settlements in Southern England', Journal of European Archaeology, 1 (1993) pp.57-75

(One of a number of papers by J.D. which emphasise the 'differentness' or 'otherness' of the British Iron Age past, and the danger of assuming it must be a familiar, known, Celtic one)

There is an article by J.D. (although minus pictures) on the Web: 'Weaving the strands of a new Iron Age'

See also:

• Nick Merriman, 'Value and motivation in prehistory; the evidence for "Celtic sirit"', in Hodder, I., (ed.) The Archaeology of Contextual Meanings, Cambridge University Press 1987, pp.111-116.

(A critical look at the evidence for an identifiably 'Celtic spirit' in the remote past)

Celtic Art

• Ruth and Vincent Megaw, Celtic Art from its beginnings to the Book of Kells, Thames & Hudson, London and New York 1989

(An excellent general work on the 'La Tene' art style, the name given to the largely abstract, 'curvilinear' (curving-line) art popularly known as 'Celtic'.)

Druids

The best books (in my opinion!) are:

• Stuart Piggott, The Druids Thames and Hudson, London and New York 1985
• Miranda J. Green, Exploring the world of the Druids, Thames and Hudson, London and New York 1997

(Druids probably had nothing to do with Stonehenge - they flourished 1,000 years after the great stones appear to have been abandoned, perhaps representing the collapse of an entirely different, earlier belief system. Similarly, most archaeologists would argue that the modern Druidic orders are a product of eighteenth century romanticism, and have no link with the real, Iron Age Druids.)