As the leader of majority party in lower house (Lok Sabha) of the Legislature, The Prime Minister is called upon and appointed by the President. During the appointment the Prime Minister has to be the member of either house of Parliament or he/she has to get elected within six months after appointment. On the advice of Prime Minister the President forms the Central Cabinet. The Prime Minister of India is real head of the Government who enjoys the executive powers and performs the functions to decide the policies of the Government. The powers of coordination among the various Ministries, heading of the Cabinet meetings resides in the hands of Prime Minister.
All the important matters related to the high offices appointments, dissolving of Lok Sabha and the declaration of emergency is adviced by The Prime Minister to the President. In short, the Prime Minister is the all-in-all of the entire government machinery.
Indian Politicians
List of Prime Ministers of India

(Born: 26 September 1932)
Term of Office: 22 May, 2004 To Till date
Political party: Indian National Congress (INC)

(Born: 25 December 1924)
Term of Office: 19 March, 1998 - 22 May, 2004 and 16 May, 1996 - 1 June, 1996
Political party: Bharatiya Janata Party (BJP)

(Born: 4 December 1919)
Term of Office: 21 April, 1997 - 19 March, 1998
Political party: Janata Dal

(Born: 18 May 1933)
Term of Office: 1 June, 1996 - 21 April, 1997
Political party: Janata Dal

(Born: 28 June 1921 Died: 23 December 2004)
Term of Office: 21 June, 1991- 16 May, 1996
Political party: Indian National Congress (INC)

(Born: 1 July 1927 Died: 8 July 2007)
Term of Office: 10 November, 1990 - 21 June, 1991
Political party: Janata Dal (S)

(Born: 25 June 1931)
Term of Office: 2 December, 1989 - 10 Nov, 1990
Political party: Janata Dal

(Born: 20 August 1944 Died: 21 May 1991)
Term of Office: 31 October, 1984 - 2 December, 1989
Political party: Indian National Congress (INC)

(Born: 23 December 1902 Died: 29 May 1987)
Term of Office: 28 July, 1979 - 14 January, 1980
Political party: Janata Party

(Born: 29 February 1896 Died: 10 April 1995)
Term of Office: 24 March, 1977 - 28 July, 1979
Political party: Janata Party

(Born: 19 November 1917 Died: 31 October 1984)
Term of Office: 14 January, 1980 - 31 Oct, 1984 and 24 January, 1966 - 24 March, 1977
Political party: Indian National Congress (INC)

(Born: 2 October 1904 Died: 11 January 1966)
Term of Office: 9 June, 1964 - 11 January, 1966
Political party: Indian National Congress (INC)

(Born: 4 July 1898 Died: 15 January 1998)
Term of Office: 27 May, 1964 - 9 June, 1964 and 11 January, 1966 - 24 January, 1966
Political party: Indian National Congress (INC)

(Born: 14 November 1889 Died: 27 May 1964)
Term of Office: 15 August, 1947 - 27 May, 1964
Political party: Indian National Congress (INC)