Texas Transportation Code [paraphrased]:

’551.101(a) – A bicyclist has the rights and duties of  motor vehicle, unless by their nature they cannot apply to a bicyclist.

’551.103(a) – A bicyclist moving slower than traffic shall ride near the right edge the roadway, unless the lane is too narrow for a bike and car, then the cyclist can take the whole lane.

’551.103(c) – Bicyclists may ride two abreast if not impeding the flow of traffic on the roadway.

’551.104(b) – At night, (1) a front white light visible 500′ and (2) a rear red reflector visible with headlamps on highbeams on from 50′ to 300′, or a red lamp on the rear visible from the distance of 500′.

’545.058(c)(3)– Bikes are exempted from the general prohibition against driving on shoulders.

Austin City Code/University of TX Regs

’12-2-13, UT Regs – A bike can be ridden on a sidewalk except on the UT Drag, on UT sidewalks, and  most of the central business district in downtown Austin.

’12-1-35 –  When road conditions allow, cars and light trucks must give bikes 3 feet when passing; big trucks 6 feet.