After the surrender of the Irish nationalists, the British government continued to keep all of Ireland under martial law, meanwhile demanding that the Irish surrender their weapons.  Many Irish civilians, who had not participated in the Rising, disapproved of the events of Easter week.  However, as the British imprisoned, court-martialed, and sentenced to death numerous Irish men and women, public opinion began to shift in favor of the Irish nationalists. 
Murphy, T. W. “Rounding up the Rebels.” Dublin after the Six Days' Insurrection: Thirty-One Pictures From the Camera of Mr. T. W. Murphy. Dublin: Mecredy, Percy and Co., Ltd., 1916, 27. [Digital Library]
All seven signers of the Proclamation of the Irish Republic were executed, among others.  Eamon de Valera, however, who had commanded forces in the Old Distillery during the Rising, was not executed. Born in America, the U.S. Consulate was able to help prevent his death.  Theodore Roosevelt tried to help ease Sir Roger Casement’s sentence, but his efforts were unsuccessful and Casement could not escape execution, despite the help of the Americans. 
Sinn Fein Rebellion Handbook, Easter, 1916: A Complete and Connected Narrative of the Rising, With Detailed Accounts … Dublin: The Irish Times, 1917, 2-3. [Internet Archive]
“Greatest Irish Meeting Ever Held in New York Denounces England’s Ruthless Murder in Cold Blood of Prisoners of War,” The Gaelic American - Vol. XIII No. 21, May 20, 1916, Whole Number 662. New York [N.Y.] : Gaelic American Pub. Co, 1916. [Digital Library]
“Casement to Die August 3. Date of Execution Set, But Friends Keep up Work to Save Life,” Issues and Events V. 5 No. 6. New York : F. J. L. Dorl, 1916, 14. [Digital Library]
Colum, Padraic. “Roger Casement,” Issues and Events V. 5 No. 15. New York : F. J. L. Dorl, 1916, 7. [Digital Library]
“Sir Roger Casement Who Laid Down His Life for Ireland, August 3, 1916,” Photograph, Roger Casement Seated Seaside. [Digital Library]
Grieved by the loss of so many men, the Irish determined to continue the work the Rising had so powerfully begun of establishing an Irish Republic. In 1917, the first national convention of the Irish government met and decided on a constitution. 
"Complete Independence is the Goal of the Sinn Fein Movement,” The Gaelic American - Vol. XIV, No. 40, October 13, 1917, Whole Number 734. New York [N.Y.] : Gaelic American Pub. Co, 1917, 3. [Digital Library]
“Ireland in the Grip of British Militarism,” The Gaelic American - Vol. XIV, No. 39, September 29, 1917, Whole Number 733. New York [N.Y.] : Gaelic American Pub. Co, 1917, 1. [Digital Library]
The next year, the government was confirmed in an election, and in 1919, the Irish government, called the Dáil Éireann, came into power.  Under the leadership of President Eamon de Valera, the Dáil remained committed to Ireland’s independence. 
Once again, the Irish had to fight for their nation from 1919-1921 in the War of Independence.  In 1922, a Treaty was at last ratified that granted Ireland independence for the twenty-six lower counties of the nation.  Some historians argue that the Easter Rising influenced the War of Independence, and thus was a significant factor in Ireland’s national liberation. 
Dail Eireann. Ireland's Elected Government: A History of the Dail Eireann: Being an Official Account of Its Establishment As the Answer of the Elected Government of Ireland to the Statement of English Propagandists That Dail Eireann Is an Organization for the Encouragement of Outrage, and Published At Dublin, Ireland, As an Official Bulletin of the Republic of Ireland. Washington, D.C.: Friends of Irish Freedom, National Bureau of Information, 1920. [Digital Library]
Poblacht Na H-Éireann War News, Number 28, Tuesday, August 1st, 1922. [Dublin? : s.n.], 1922. [Digital Library]
Poblacht Na H-Éireann War News, Number 56, Tuesday, September 12th, 1922. [Dublin? : s.n.], 1922. [Digital Library]
Sinn Fein. Clar: An Feith-Leith Ard-Fheis, a Bheidh Ar Siul Sa Seomra Cruinn I DTig an Ard Mheire Ath Cliath, Dia Mairt, an 7adh Feabhra, 1922. Dublin : Dollard, 1922. [Digital Library]
2. The Irish Times, in Sinn Fein Rebellion Handbook, Easter 1916: A Complete and Connected Narrative of the Rising, with Detailed Accounts of the Fighting at all Points in Dublin and in the Country (Dublin: The Irish Times, 1916), 34-40.
4. Boyle, The Irish Rebellion of 1916, 232-233; Warre B. Wells and N. Marlowe, A History of the Irish Rebellion of 1916 (Dublin and London: Maunsel and Company, Limited, 1916), 203-204; 1916 Rebellion Handbook (Dublin: The Mourne River Press, 1998), 7.
11. BBC, “Aftermath: The Anglo-Irish War,” Easter 1916: From Home Rule to Independence, September 24, 2014, http://www.bbc.co.uk/history/british/easterrising/aftermath/af04.shtml.
12. BBC, “Aftermath: The Treaty,” Easter 1916: From Home Rule to Independence, September 24, 2014, http://www.bbc.co.uk/history/british/easterrising/aftermath/af06.shtml.
“Military Massacre Under the Rule of an English Courtmartial,” The Gaelic American - Vol. XIII No. 20, May 13, 1916, Whole Number 661. New York [N.Y.]: Gaelic American Pub. Co, 1916, 1. [Digital Library]