Hello, I am writing a paper for international law course can someone please revise my intro? thank you.

It is ordinarily accepted among all nations that territorial jurisdiction is based on the fact that a crime is committed within their territory. However, sometimes they also exercise jurisdiction because the crime was committed abroad by one of their nationals or because the victim of the crime was a national of the state.
For instance, in the federal court case United States v. Yanez, in which five men hijacked a Jordanian airliner. Among these passengers were two American citizens who were apparently not the target of the terrorist activity. Hijackers latter released the passengers and blew up the aircraft. The defendant was lured into international waters and brought to the United States, where he was convicted of conspiracy, hostage taking, and air piracy (Smit1118). Thus, in this case jurisdiction was held under the Hostage Taking Statute of the United States, providing jurisdiction on the nationality of the victim, and under sect. 32 of the Aircraft Piracy Statute, adopted from traditional international legal bases of the universal and passive personality principle (1120).

The first paragraph is OK, but needs work -- however, the second is far too factual for an introduction. Here are some webpages on how to write introductions:

http://leo.stcloudstate.edu/acadwrite/intro.html

http://grammar.ccc.commnet.edu/grammar/intros.htm

In that first paragraph, you need to do something about the wordiness -- that is, using too many words to say something simple. You also need to make sure you have no vague references to anything, since it's the beginning of your paper and so far there's nothing to refer to! And you need to be clear on whatever you're defining.

It is ordinarily accepted among all nations<~~Are you absolutely sure that "all nations" agree on this? that territorial jurisdiction is based on the fact that a crime is committed within their territory.<~~The definition of "territorial jurisdiction" is solely based on crimes that have been committed?? However, sometimes they also exercise jurisdiction because the crime was committed abroad by one of their nationals or because the victim of the crime was a national of the state.

http://grammar.ccc.commnet.edu/grammar/concise.htm
Scroll about halfway down this webpage to see about the "the fact that" phrasing and how to fix it.

It is ordinarily accepted among nations that territorial jurisdiction is based on a crime that is committed within the territory of the sovereign state. However, sometimes states also exercise jurisdiction because the crime was committed abroad by one of their nationals or because the victim of the crime was a national of the state.

Territorial jurisdiction is a fundamental concept in international law, based on the principle that a crime committed within a nation's territory falls under their jurisdiction. However, there are instances when a nation exercises jurisdiction over a crime committed abroad by one of their nationals or when the victim of the crime is a national of that state.

To illustrate this point, the federal court case United States v. Yanez can be examined. In this case, five individuals hijacked a Jordanian airliner, which also had two American citizens on board, who were seemingly not the targets of the terrorist activity. The hijackers later released the passengers and destroyed the aircraft. The defendant was eventually brought to the United States, where he faced charges of conspiracy, hostage taking, and air piracy.

In this particular case, jurisdiction was pursued under the United States Hostage Taking Statute, which grants jurisdiction based on the nationality of the victim, and under section 32 of the Aircraft Piracy Statute, which draws from traditional international legal principles such as the universal and passive personality principle.

It's important to note the specific legal provisions that were invoked to establish jurisdiction in this case, highlighting how international law allows for the exercise of jurisdiction beyond mere territorial boundaries.