The Jewish Front, headed by Baruch Marzel, is an offshoot of the Kach group, whose principles Israel's Supreme Court said incited racism.
Kach was outlawed by both the Israeli and US governments in 1994.
The Jewish Front advocates the forced expulsion of Arabs from "the land of Israel".
According to Beny Elyaho, a co-founder of the party, the expulsion of non-Jews would resolve all of Israel's political, economic and social problems.
"Our party calls for cleansing the region extending from the River Jordan to the Mediterranean from the goyim (non-Jews) and thus guaranteeing a Jewish majority of no less than 90% throughout the land of Israel," he was quoted as saying during a party meeting in West Jerusalem last year.
Marzel has called parties willing to negotiate with the Palestinians "traitors" and "criminals" and says the Israeli military should assassinate Uri Avnery, leader of the Gush Shalom peace activist movement.
Another party, Herut, headed by Michael Kleiner, advocates legislation that would offer Palestinians and other non-Jewish citizens of Israel "financial inducements" to emigrate to the Arab world and elsewhere.
Herut, meaning freedom in Hebrew, maintains the vision of Eretz Yisrael Hashlema (or Greater Israel) encompassing all mandatory Palestine where non-Jews are accorded inferior or no rights by virtue of being non-Jewish.
Israelis overseas went to the
polls on Wednesday
The party also views nearly all of Jordan as part of Israel which "one day" could be "re-incorporated into Israel".
According to the party platform, Herut stands for increasing the "Jewish bond" with the Temple Mount, a euphemism for demolishing al-Aqsa mosque and other Muslim holy places in Jerusalem.
The National Union (Haichud Haleumi) party, comprised of the Settler Party, the Mifdal, and other Jewish groups, also calls for the resettlement of Palestinian refugees in Arab countries and elsewhere.
No Palestinian state
The party headed by Benjamin Elon, a former Israeli cabinet minister, also opposes the creation of a Palestinian state.
"The National Union pledges that another political entity will not rise between Jordan and the sea. The funds which were being transferred to the Palestinian Authority by the government, will henceforth be used for reparations for the damage Israel has suffered during the period of terror," the party's website says.
It advocates the creation of a Talmudic Jewish kingdom whereby non-Jews in general, and Palestinians in particular, are treated as "water carriers and wood hewers" in the service of Jews.
"Our party calls for cleansing the region extending from the River Jordan to the Mediterranean from the goyim (non-Jews) and thus guaranteeing a Jewish majority of no less than 90% throughout the land of Israel"
Beny Elyaho, co-founder,
the Jewish Front
Yisrael Beitenu (Israel is Our Home), headed by Russian immigrant Avigdor Lieberman, is mainly a "Russian party" since most of its support come from Russian-speaking Jewish immigrants who moved to Israel in the late 1980s and early 1990s.
Lieberman advocates "population transfer" of Israel's Arab citizens. And according to the Israeli daily Haaretz, he also calls for ignoring the Palestinian Authority and drawing Israel's final borders with Egypt, Jordan and the road map quartet of the UN, the US, the EU and Russia.
Arab MPs in the Knesset have accused Lieberman of racism for seeking to expel Israeli Arabs, some of whom he has called extremist elements.
Likud, headed by Benyamin Netanyahu, the former prime minister, has drifted further to the right since Ariel Sharon, the Israeli prime minister who now lies in a coma, left the party to form the Kadima (Forward) party in November 2005.
Likud has called for the annexation of the bulk of the West Bank (at least 50% of the occupied Palestinian territories) and granting Palestinians a limited autonomy which could be allowed to evolve into a mini-state in the future.
Benyamin Netanyahu's Likud has
moved further to the right
According to its campaign website, Likud also opposes relinquishing control of the Golan Heights to Syria and firmly opposes Kadima's policies of unilateral withdrawals.
Israeli law states that no one can stand for elections to the Knesset if his goal or actions "expressly or by implication", includes "incitement to racism".
But Fawaz Kamal, the head of the Israeli government press office, told Aljazeera:
"The judicial system in Israel saw that there was no legal grounds for outlawing these parties or barring them from participating in the elections as long as they don't include their purported racist attitudes and views in their respective platforms."
Talab al-Sani'e, a Knesset member and lawyer, said: "the Israeli High Court has effectively ignored this law and decided to let the people (voters) decide".
"Only in extreme cases, such as in the case of the Kahana party, which openly called for the expulsion of the Arabs, did the court decide to ban that party."
However, Kamal and al-Sani'e could not explain why other parties such as the Jewish Front, which also advocate the forced expulsion of Arabs, have been allowed to run.
Kadima, led by Ehud Olmert, the acting prime minister and staunch Sharon ally, stands at odds with Likud and other right wing parties.
It calls for the continuation of the peace process with the Palestinians but simultaneously "continuing to wage an unremitting war against terrorism".
It calls for a determination of Israel's permanent borders based on a peace deal and also says a solid Jewish majority is crucial to the future security of Israel.
Olmert's Kadima looks set to win
a third of the Knesset seats
The Labour party, led by Amir Peretz, has various approaches to the peace process, with some members calling for all out war against "terrorist" organisations and others saying Israeli tactics have been heavy handed.
Labour believes continuing the peace process is crucial and in recent days Peretz announced his platform to compensate settlers willing to leave West Bank settlements prior to any withdrawal.
There are also parties such as Meretz, which calls for an end to occupation and a permanent peace deal based on the 1967 borders.
Meretz is headed by Yossi Beilin, a former economy and planning minister and a current member of parliament.
"Today, [slain prime minister Yitzhak] Rabin's legacy is clearer than ever: Reaching peace requires a historic compromise. And only a historic compromise will ensure the full equality of Israel's citizens, and thus the fulfilment of the Zionist dream," Beilin says in his party's charter.
He calls for a two-state solution with two capitals in Jerusalem. In 2003, his party won six seats.
According to an Israeli army poll, Kadima is likely to win over 42 seats (out of 120 seats making up the Israeli Knesset), with Likud gaining some 15-16 seats, and Labour some 14 seats.
Right wing and religious parties could muster as many as 55 seats, only 6 seats short of an absolute majority.
Ira Sharkansky, a professor in Hebrew University's political science department, told Aljazeera.net the presence of so many right wing and religious parties hinders the democratic process.
He said "this is the way it is in Israel", adding that it is very difficult for the judicial system in Israel to "outlaw a political party".
"They allowed these parties just as they allowed an Islamic party to run," said Sharkansky.
There are four Israeli Arab parties running in the upcoming elections - Hadash, Balad, Movement for Arab Renewal, and the United Arab List, run by Shaikh Ibrahim Sarsur.
All four parties call for the implementation of UN Security Council resolutions on Israeli withdrawal to the 1967 borders, the establishment of an independent Palestinian state, and more rights for Israeli Arabs.
Election posters for Hadash in the
Arab-Israeli town Umm el-Fahem
They also advocate East Jerusalem as a future capital of the Palestinian state.
Current Arab Knesset member and leader of Movement for Arab Renewal, Ahmed Teibi, who is contesting the elections, believes the growth of "racist right-wing factions" is a sign of how Israeli society is leaning.
"The mushrooming of these racist right-wing factions is an honest and representative reflection of Israeli Jewish society. It is a society that is increasingly racist, bigoted and chauvinistic.
"How can we think otherwise when a majority of Jews here advocate the expulsion of non-Jewish citizens in Israel?"