State law says landlords must fix anything that threatens a tenants health or safety.
In Texas, A/C counts. If it happens to you notify the landlord in writing.
You can hand deliver the letter but mail a copy via certified mail as well.
The next step depends on who you are.
If you have small children or elderly in your home, call the city within one hour so they can send inspectors out.
If everyone's healthy wait 24 hours before calling the city.
You may be tempted to not pay your rent, but that puts you at risk for eviction, make sure you stay fully paid up on all your rent.
If you follow all these steps and still don't have air you can break you lease and sue for damages, just consult an attorney before you do.