Son of John Erskine of Carnock (1662-1743)1 and Anna Dundas (d. 1723). Married (1719) to Margaret Melville. Married (1729) to Anne Stirling. He had at least 7 children.
Erskine became a member of the Faculty of Advocates in 1719, and Professor of Scots law at the University of Edinburgh in 1737, a post he kept until his retirement from public life in 1765. In 1754 he published The Principles of the Law of Scotland which quickly became a standard textbook in Scots law. At the time of his death he was working on The Institutes of the Law of Scotland, which was completed posthumously by friends and colleagues and was published in 1773; it remained an authority on Scots law for several decades following its publication.
Boswell possibly attended some of Erskine's lectures while at the University of Edinburgh in the late 1750s or early 1760s. Boswell considered translating Erskine's Institutes into latin, with the help of Professor Trotz, during his stay in Utrecht in 1763-64.
18th and 19th century editions of Erskine's Principles and Institutes are usually available via used books search engine such as AbeBooks.