If I have someone harrassing me through email(hotmail), how do I find
out who it is. I have their IP address information. Which I will
Supply if you need it.

Its pretty easy to figure out who owns the IP address, but that
"owner" will probably be the internet service provider for the user. 
You can reverse to the owner at:
http://www.arin.net/whois/index.html
just enter the IP address.  From that point, the owner is responsible
for managing their own pool of ip addresses.  Most companies use a
service that dynamically assigns an available ip address to a user
when they connect.
This means that a given ip address will probably not be the same
person over time (although the persone MIGHT have a static IP address
it is doubtful).  The lookup should list contacts, and you can try to
email them explaining that one of their users is harrassing you, but
it is doubtful that you would actually be able to get a name.

Hi nycman,

If the person is harrassing you through your e-mail account, why not
just block their incoming e-mails? Most e-mail providers give you
"blocking" options which will put an end to the harrassment.

The IP address will be from one of Hotmail's servers, and of no use.

Display the full header of the e-mail and look for the X-Originating
IP. All Hotmail e-mails display this IP, as determined by Hotmail
servers at the time of use. The user could be employing a proxy,
however. From the X-Originating IP, you can run a reverse DNS lookup,
and possibly come up with an ISP. Beyond that point, it would very
likely require access to ISP records to determine which customer was
assigned to that IP at that particular moment. Such records are seldom
freely available.

Hotmail, and most ISPs, have an Abuse department which can be
contacted with complaints. You should use the Forward function of your
e-mail client, showing the complete header, with a note at the top of
the e-mail explaining your dilemma. It can be helpful if you identify
and quote the portion of the ISP's Terms of Service that the e-mail
violates.

--- l

Please read an answer I previously gave and might help you:
http://answers.google.com/answers/main?cmd=threadview&id=50182