What are the basic elements of judaism?

Answer 1

Though it may have an associated culture and one or more associated languages, the traditional definition of Judaism is the observance of the Torah, which is why dictionaries define Judaism as "the religion of Moses." In this sense, the word "Torah" is meant in its wider meaning, which includes the Tanakh, the Talmud, and other classical Jewish texts.
The philosophy of Judaism is that this world is a purposeful creation by God, in which all people are tested concerning their use of free-will. We possess a soul which lives on after the body dies and is held responsible for the person's actions. Anyone who is worthy, Jewish or not, can merit reward in the afterlife.
Some examples of the commands:
Belief in God
Putting on Tefillin (phylacteries) in the morning
The sukkah-booth during Sukkot
Avoiding leavened products in Passover
Keeping kosher
Not eating on Yom Kippur
Not working on the Shabbat
Paying workers on time
Marital rights for one's wife
The Ten Commandments
Helping someone who is in danger
Counting the days of the Omer
Returning lost objects when feasible
Wearing the tzitzith-garment
Affixing a mezuzah to the door
Learning Torah
Marrying and having children
Educating one's children in Judaism
Giving tzedakah (charity)
Honoring one's parents
And many more.
The laws have various reasons. Some (such as the Passover) serve to reenact or remember events of our history.
Some (such as saying the Shema-prayer) serve to reiterate our belief in God.
Some of the laws (such as those of ritual purity and kosher food) serve to sanctify us.
Some (such as the laws of torts) serve to maintain an orderly and just society.
Some (such as the law against breaking a vow) serve to prevent bad character traits.
Some (such as the command to offer help) serve to engender good character traits.
And all of the commands serve to subjugate us to God's will (especially those commands for which no explanation is easily apparent).
Note that the Torah "as is" isn't exactly what Judaism observes. Rather, It's the Torah together with the details provided in the Talmud, which is the Oral Law that was handed down together with the laws of Moses. Otherwise, the verses of the Torah often lack enough detail to be fulfilled as is.

Answer 2

All the hundreds of mitzvoth (commands), principles and beliefs of the Torah.

Though it may have an associated culture and one or more associated languages, the traditional definition of Judaism is the observance of the Torah, which is why dictionaries define Judaism as "the religion of Moses." In this sense, the word "Torah" is meant in its wider meaning, which includes the Tanakh, the Talmud, and other classical Jewish texts.
The philosophy of Judaism is that this world is a purposeful creation by God, in which all people are tested concerning their use of free-will. We possess a soul which lives on after the body dies and is held responsible for the person's actions. Anyone who is worthy, Jewish or not, can merit reward in the afterlife.
For fuller detail, see the Related Links.Link: The basic beliefs of Judaism

Link: The practices of Judaism

Link: The principles of Judaism

Link: The ethics of Judaism

Link: How Judaism began

Link: The texts of Judaism

Answer 3

Belief in God, the Torah, the soul and responsibility for one's actions.

Answer 4

See the attached Related Question for four informative links.