These are some general works.

Title:		Modern Ireland 1600-1972
Author:		R.F. Foster
Publisher:	Penguin
ISBN:		0-14-013250-3

Title:		Ireland Since the Famine
Author:		F.S.L. Lyons
Publisher:	Fontana
ISBN		0-00-686005-2

Title:		Ireland 1912-1985: Politics and Society
Author:		J.J. Lee
Publisher:	Cambridge University Press
ISBN:		0-521-37741-2

Title:		Oxford History of Ireland
Author:		R.F. Foster (Ed.)
Publisher:	Oxford University Press
ISBN:		0-19-822970-4 (hardback)

Title:		The Making of Modern Ireland 1603-1923
Author:		J.C. Beckett
Publisher:	Faber & Faber
ISBN:		0-571-18036-1 (0-571-18035-3)

Title:		A History of Ulster
Author:		Jonathan Bardon
Publisher:	Blackstaff Press
ISBN:		0-85460-476-4 ( 0-85640-466-7 hardback )

Title:		Early Medieval Ireland: 400 - 1200
Author:		Dáibhí O'Cróinín
Publisher:	Longman
ISBN:		0-582-015650 ( 0-582-015669 cloth )

One book that people mention a lot in connection with early Ireland is

Title:		How the Irish Saved Civilization
Author:		Thomas Cahill
Publisher:	Doubleday Books
ISBN:		0-385-41849-3 (hardback or paperback?)


[ The publishing information given is for the paperback editions unless
  otherwise specified. ]

	One online resource worth mentioning is the CELT Irish Electronic
	Text archive at UCC, which has a variety of texts available for
	reading on the web or download.
	See http://www.ucc.ie/celt/