The most comprehensive information for admissions can be found at the BE A LONGHORN website http://bealonghorn.utexas.edu/. The links below will take you directly to specific admission information based on the time of admission you are seeking.
First Time Freshman Admissions
http://bealonghorn.utexas.edu/freshmen
Transfer Admissions
http://bealonghorn.utexas.edu/transfer/admission
First Time International Undergraduate Admissions
http://bealonghorn.utexas.edu/international/first-time
International Transfer Undergraduate Admissions
http://bealonghorn.utexas.edu/international/transfer/apply
GRADUATE ADMISSIONS
Click on the link above for Graduate Admissions information.