Vector Analysis is a textbook by Edwin Bidwell Wilson, first published in 1901 and based on the lectures that Josiah Willard Gibbs had delivered on the subject at Yale University.

The book did much to standardize the notation and vocabulary of three-dimensional linear algebra and vector calculus, as used by physicists and mathematicians.

The final eight pages develop bivectors as these were integral to the course on the electromagnetic theory of light that Professor Gibbs taught at Yale.

Hermann Grassmann had introduced basic ideas of a linear space in 1844 and 1862, and W. K. Clifford published Elements of Dynamic in 1878, so as Gibbs was teaching physics in the 1880s he took these developments into consideration for his students.

He had learned about quaternions from James Mills Peirce at Harvard, but Dean A. W. Phillips persuaded him to take Gibbs's course on vectors, which treated similar problems from a rather different perspective.

Wilson wrote the book by expanding his own class notes, providing exercises, and consulting with others (including his father).