which institution did he study law from?
He read law at his father's office
Thomas F. Bayard
Bayard was unsatisfied with his progress at the firm and returned to Wilmington to read law at his father's office.

Bayard was admitted to the bar in 1851, the year his father was elected to the United States Senate. Thomas took on greater responsibilities in the family law office and rose quickly in the legal profession.
who was thomas f. bayard? An American lawyer, politician and diplomat from Wilmington, Delaware
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Thomas F. Bayard [SEP] Early life and family
Thomas took on greater responsibilities in the family law office and rose quickly in the legal profession. In 1853, after the election of Democratic President Franklin Pierce, Bayard was appointed United States Attorney for Delaware. He spent only a year in the position before moving to Philadelphia to open a practice with his friend William Shippen, a partnership that lasted until Shippen's death in 1858. While in Philadelphia, Bayard met Louise Lee, whom he married in October 1856. The marriage produced twelve children.