Within Judaism there are many different groups: Hasidic, Orthodox, Conservative (Masorti), Reform, Progressive, Liberal. (It is important to remember that some of these names have different meanings in the USA than in the UK.)
Differences between the groups derive from both belief and practice. There may be differences over the status of the Torah and also of the Talmud.
Some groups look towards a very traditional approach to the faith, believing essentially that nothing should ever change. Others are more progressive in their thinking and feel that Judaism should adapt to the world in which it finds itself and, importantly, that it is possible to do this without compromising the faith. Some Jews believe that the Torah can be questioned and may be interpreted for the 21st century.
There are differences over responses to the State of Israel.
There are also divisions over the extent to which kashrut (lawful in terms of food, clothes, money and objects) must be observed; over whether women can sit with men; whether women can read from the Torah in public; whether women can be rabbis; whether children with a Jewish father and gentile mother should be regarded as Jewish; whether a divorced woman can remarry if her husband does not grant her a ‘get’, a religious divorce document; over whether women can become rabbis; whether women must continue to visit a mikveh (ritual bath) after menstruation, and whether it is permissible to drive to the synagogue on the Sabbath. These and many other issues continue to divide the world Jewish community.