Burnet is a city in and the county seat of Burnet County, Texas, United States. Its population was 6,436 at the 2020 census. Both the city an…Burnet is a city in and the county seat of Burnet County, Texas, United States. Its population was 6,436 at the 2020 census. Both the city and the county were named for David Gouverneur Burnet, the first president of the Republic of Texas. He also served as vice president during the administration of Mirabeau B. Lamar.
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