The Jews heard the first two commandments directly from G-d, but they couldn't take the Divine revelation directly, so they asked Moshe to get the rest of the Torah for them.

Until this Parsha, the Torah only gives a few commandments - starting with the laws of Rosh Chodesh -- the new moon -- and Shabbat, etc.

In parsha Mishpatim several additional commandments are given.

There are three types of commandments: Mishpatim are civil laws, laws with a human understandable reason, that people even might make up themselves.

Another type is Chukim, which are laws without a completely human understandable reason. An example of a choke is the concept of tuma (impurity) and tahara (purity). Such laws, as the laws of family purity (Taharas Hamishpocha), which are a G-d given gift to the Jewish people, are Chukim.

A third type of commandment is Eidus (witness), where, by performing these commandments we testify that G-d did something. For instance, resting on Shabbos is testimony that G-d created the world in six days and rested on the seventh day.

This parsha is referred to as Mishpatim - and begins by giving some of the first type of commandment -- Mishpatim - Civil Laws.

• In the first aliyah we are given some laws of servants, laws of a husband's obligation to his wife in the manner of food, raiment, and conjugal rights, laws of intentional and unintentional manslaughter, and laws of kidnapping, and other injuries.
  
  
• The second aliyah contains some laws of various kinds of assault -- the expression "an eye for an eye, a tooth for a tooth" is here. Also in this aliyah are laws of a goring ox, open pits, and self-defense when a thief breaks in.
  
  
• The third aliyah contains some laws of monetary damages, sorcerers, bestiality, and idol-worship.
  
  Also here are laws not to afflict the stranger, the widow, and the orphan, and for a Jew not to charge interest on a loan to another Jew.
  
  
• The fourth aliyah has laws of blasphemy (against G-d, rulers, and judges), laws of sanctifying the first-born son (the pidyon haben ceremony), first of the harvest and of cattle. Also here are some laws of kashrus -- the word "trefa" appears here. The law of uttering a false report (Rashi says: also accepting a false report) and other matters of judicial process are also given here.
  
  Here are also the laws concerning seeing your enemy's animal going astray - you should bring it back to him. Similarly, if you see your enemy's animal under a burden, you should help.
  
  
• The fifth aliyah continues judicial matters, including not taking a bribe, because the Torah says that a bribe blinds those that have sight.
  
  Rashi explains an interesting judicial law: if someone is acquitted, and as he's leaving the court someone runs up and says they have evidence against him, we should ignore the evidence and not return to court. But if a person is found guilty and is leaving the court and someone runs up and says they have evidence in favor of him, we should return him to court to hear the evidence.
  
  The mitzvah of the Shmittah year is explained: wherein for six years we should work and harvest the land but in the seventh year let the land rest.
  
  The Shabbos is explained as six days we shall do our work but on the seventh day we, our cattle, our servants, and the stranger within our gates shall rest.
  
  This aliyah says we shouldn't mention the name of other gods. Rashi says that this includes giving street directions by mentioning churches as landmarks.
  
  The three festivals of Pesach, Shavous, and Succos are given here.
  
  We are not allowed to cook meat with milk. Rashi says this matter is mentioned three times in the Torah to teach three things about milk and meat: that we can't eat them together, we can't cook them together, and we can't even benefit from them combined (like selling it or giving it to a pet, even if we didn't cook it or eat it ourselves).
  
  
• In the sixth aliyah, after all the mishpatim just discussed, G-d says that He's going to send an angel before the Jews and bring them to the place prepared for them. The Jews should hearken to Him and not rebel against Him, and if they do so, G-d will be an enemy to the Jews' enemies.
  
  And when the Jews get to the land where they're going they should not bow down to the gods worshipped there nor serve them nor do after their doings, but instead overthrow them and serve G-d, and G-d will bless them and remove sickness from their midst.
  
  
• The seventh aliyah continues the promise to the Jews if they follow G-d's laws: there will be no barrenness or miscarrying in their land and G-d will fulfill their days.
  
  G-d will send terror before the Jews come to the land to drive out their enemies little by little (little by little so the land won't become overrun with wild animals by being cleared out quickly, and then gradually become filled with the Jewish nation).
  
  Moshe offers sacrifices and sprinkles the blood on the people, which is considered the blood of the covenant like a bris mila.
  
  G-d calls Moshe up to the mountain to get the 2 luchos (tablets). Moshe goes up mount Sinai and stays there for 40 days and 40 nights.