The Israeli legal system is based on common law, also known as case law or precedent law, which is based on decisions of courts and judges, but it has some parts of civil law as well.

This means that Israel does not have a formal Constitution, even though it was decided when the State of Israel was founded, that one would be written. In this way, the Israeli laws are similar to the ones in the United Kingdom, but in recent years, the Israeli court system and laws have also been heavily influenced by the laws in the USA and Canada.

The Common Law system was implemented by the British when they were governing Palestine before the independent state was founded, and several things have never been changed since then. Even some older laws, dating back to the Ottoman rule of Palestine, still remain in the Israeli law.
This is why Israeli law can be said to be as diverse as the history of the country itself.

As for the court system, there are several courts in Israel that influence the current laws. The Shalom Court, Beit Mishpat HaShalom in Hebrew, is a smaller court that handles only civil cases, where the disputed amount is less than 2,5 million NIS (New Israeli shekels, the currency of Israel), but it never deals with issues relating to ownership of land or with criminal cases where the sentence could be over 6 years of prison.
The Shalom Courts are based in the towns themselves, and most Israeli towns have one.
The District Court, or the Beit Mishpat Mehozi in Hebrew, deals with civil as well as criminal matters that do not fall under the jurisdiction of the Shalom Courts. It also deals with disputes related to ownership of land. People can also appeal sentences in the Shalom courts to the District Court.
Currently, there are 6 Disctrict Courts in Israel: in Jerusalem, Tel Aviv, Haifa, Petach Tikva, Beersheva and in Nazareth.
The Israeli Supreme Court, the Beit Mishpat Elyon, mostly deals with appeals from the District Courts, but also hears cases that do not fall under the jurisdiction of the District Courts, including political cases and international cases.
There are also several Labour Tribunals in Israel, that deal with all cases related to labour law, for instance cases between an employee and an employer.
Interestingly enough, Israel also has religious tribunals, and some very specific legal matters, such as cases where marriage and divorce is discussed, and so on, are judged by the religious tribunals. Since the population of Israel is multi-religious, there are several religious tribunals for different religions, including one for the Jewish community, one for the Muslim community, one for the Catholic Christian community, and so on.