Capital Metro
With Capital Metro's website, you can easily plan your bus/train trip!  Type in your address, and the address of the place you are going, and you will get information about all the available routes you can take.  You can buy a pass for a day, a week or a month. 
There are many buses with stops near Aston International Academy.  There is also a light rail stop very near the school: 

• Bus route 350 stops: Airport/52nd and Airport/53rd Street
• Metrorail Highland Station stop

https://www.capmetro.org/

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Ride-Share Companies
Ride-share companies are a popular transportation choice in Austin.  Install the app on your phone, and you can request a car any time, or reserve one for later. Uber and Lyft are two that we recommend.
https://www.uber.com/cities/austin/
https://www.lyft.com/rider/cities/austin-tx

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Taxi Services
Taxis are still a good choice if you do not want to use a ride-share company. Here is a company that we recommend.
https://flit.co/cities/austin