Israel voters delivered an inconclusive result in the 10 February election - giving the two leading parties Kadima and Likud 28 and 27 seats respectively.
It is Likud's Benjamin Netanyahu who has been invited to try to form the next Israeli government because he has the support of the right-wing and religious parties that make up a majority of the parliament.
How will a government be formed?
Israel's electoral system has always resulted in coalition governments, with no party ever winning the 61 seats required for a straight majority in the 120-member Knesset.
Normally the leader of the party with the most seats is offered the chance to form a governing coalition - but only if they are seen as most likely to succeed.
With Tzipi Livni only one seat ahead of Benjamin Netanyahu, and right-leaning parties holding 65 seats compared to 55 for centrist and left-wing parties, Israeli President Shimon Peres has invited Mr Netanyahu to try to form the next Israeli government.
He has six weeks to do so, starting on 20 February.
The party in third place - Yisraeli Beiteinu led by Avigdor Lieberman - firmly backed Mr Netanyahu as long as he formed a "wide" government including the three main parties.
Mr Peres has indicated that he strongly prefers a broad, power-sharing government.
Ms Livni has indicated that she would rather go into opposition than provide what party officials have called a fig-leaf for a right-wing Israeli administration.
Why were the elections called?
The road to elections began when outgoing Prime Minister Ehud Olmert announced he would resign in the face of multiple corruption investigations. Foreign Minister Ms Livni won primary elections for the leadership of Mr Olmert's centrist Kadima party in September 2008.
She then had the opportunity to form a governing coalition and become the next prime minister. But she could not reach an agreement to keep the religious party Shas in the government and opted instead to go to fresh elections.
What do the main parties stand for?
Kadima backs continuing peace talks aimed at achieving a two-state solution, and has held indirect talks with Syria over the return of the Golan Heights.
Feb 2001: Ariel Sharon elected prime minister
Aug-Sept 2005: Withdrawal from Gaza and four West Bank settlements, Binyamin Netanyahu resigns as finance minister
Nov 2005: Sharon resigns from Likud and forms Kadima
Dec 2005: Benjamin Netanyahu elected Likud leader
Jan 2006: Sharon suffers major stroke, Ehud Olmert becomes caretaker PM
March 2006: Kadima wins elections and later forms coalition with Labour
July 2006: Israel-Lebanon war breaks out
May 2007: Report criticises Olmert's handling of war. Calls for resignation.
July 2008: Facing corruption probe, Olmert announces plans to step down
September 2008: Tzipi Livni elected to lead Kadima
October 2008: Livni announces coalition bid failed
Dec 2008: Operation Cast Lead launched on Gaza
Feb 2009:10 February 2009: Elections held
The party was formed in 2005 after Likud was split over Prime Minister Ariel Sharon's unilateral pullout from Gaza and dismantling of settlements in the Israeli-occupied territory.
It was meant as a vehicle for further unilateral withdrawals which obviated the need for peace talks. However in November 2007 Kadima locked step with US President George W Bush in his last-year push for Palestinian statehood through negotiations.
Despite it "pro-peace-deal" agenda Kadima has presided over two wars in its three years in power - the 2006 Lebanon war and the recent operation against Hamas in Gaza.
Likud stands further to the right. It has been critical of the Kadima-led peace talks with the Palestinians and wants to sets aside talk about a Palestinian state. Mr Netanyahu, a former finance minister as well as prime minister, stresses the need for economic development in the Palestinian territories in order to calm the situation.
Likud says the Kadima-led government halted the Gaza offensive too early, and opposes any withdrawal from the Golan Heights or division of Jerusalem.
Yisrael Beiteinu is a champion of Jewish settlers on land Israel occupied in the 1967 war. It is seen as the scourge of the Arab minority who trace their roots back to the historical Palestine that existed before the establishment of the Israeli state in 1948.
Mr Lieberman favours Israel jettisoning swathes of territory inhabited by mainly Arab families and annexing blocs of Jewish settlements in the West Bank. He is also proposing a new loyalty test for Arab citizens of Israel.
What is Israel's electoral process?
It is a system of proportional representation, where voters choose a party rather than an individual. Seats are allocated in proportion to the number of votes each party receives beyond a threshold of two percent.
The system usually empowers a plethora of minority parties in parliament, including a number of Jewish religious groupings which can wield disproportionate influence.
Thirty-four parties stood in the 2009 poll and 12 crossed the threshold. Seven of these parties had five or fewer seats
Candidates are allocated seats according to the order in which they appear on their party's list. The head of the list is often the leader of the party and seen as the party's candidate for prime minister.
All Israelis over 18 - some 5.3m people - are eligible to vote at 9,263 polling stations.
What is the likely impact on the peace process?
Whoever is elected will have to balance right-leaning voters and - most likely coalition partners - against pressure to push forward with meaningful negotiations from the new US President Barack Obama.
Many other factors which will influence peace negotiations remain uncertain, including the outcome of talks aimed at securing a lasting ceasefire in Gaza and also the standing of Palestinian Authority President Mahmoud Abbas, Israel's negotiating partner.
The PA is embroiled in a long-standing feud with Hamas. The militant group says it no longer recognises Mr Abbas's authority as his term has expired, and wants the PA to end its talks with Israel.
Even if Israel and the PA could reach a deal, as things stand, Hamas would be strongly opposed to it.