Texas issued privateering commissions to several ships in 1835 and 1836, and in January 1836 it also purchased four schooners - the Liberty, the Independence, the Invincible, and the Brutus. Captain Charles E. Hawkins was named the commodore of the Texas Navy on March 12, 1836.

The Navy quickly disintegrated. The Liberty captured one ship but was seized in July 1836 when the Texas government couldn't pay for its repair bill. The Independence was captured in April 1837. The Invincible was destroyed after running aground in August 1837. The Brutus was lost in a storm in October 1837.

Texas built a second small navy in 1839. President Houston tried to dissolve the navy and sell the ships in 1843, but public outcry forced him to stay his hand.

This handful of ships (and a larger number of privateers) didn't have a great operational history, but in part that's because their mere existence forced Mexican ships to keep at arm's length. They helped to keep Santa Anna's forces hungry and exhausted during the Texas War of Independence, and they prevented Mexico from overwhelming Texas during their ongoing low-intensity war over the next few years.

A really great short overview can be found in the online Handbook of Texas, and for a longer treatment read Jonathan W. Jordan's Lone Star Navy: Texas, the Fight for the Gulf of Mexico, and the Shaping of the American West.