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
https://admissions.utexas.edu/apply/freshman-admission
Transfer Admissions
https://admissions.utexas.edu/apply/transfer-admission
First Time International Undergraduate Admissions
https://admissions.utexas.edu/apply/freshman-admission#fndtn-t146-international-applicants
International Transfer Undergraduate Admissions
https://admissions.utexas.edu/apply/transfer-admission#fndtn-t147-international-applicants
GRADUATE ADMISSIONS
Click on the link above for Graduate Admissions information.