From the Texas Transportation Code:
Sec. 551.101. RIGHTS AND DUTIES.
(a) A person operating a bicycle has the rights and duties applicable to a driver operating a vehicle under this subtitle, unless:
(1) a provision of this chapter alters a right or duty; or
(2) a right or duty applicable to a driver operating a vehicle cannot by its nature apply to a person operating a bicycle.
(b) A parent of a child or a guardian of a ward may not knowingly permit the child or ward to violate this subtitle.
Want to learn more about what laws apply to you as a cyclist?
Texas Transportation Code, Chapter 551: Operation of Bicycles, Mopeds and Play Vehicles
Texas Transportation Code, All sections (Go to the bottom of the page. Click on the + sign next to Texas Statutes, then the + sign next to Transportation Code.)
Austin Cycling Bylaws: Austin City Code, Chapter 12-2. Bicycles
Ticketable bicycle violations and their associated costs: City of Austin
Austin’s Safe Passing / Vulnerable Road Users Ordinance (PDF file)