Invariant theory is a subject within abstract algebra that studies polynomial functions which do not change under transformations from a linear group. John Hilton Grace (1873-1958) was a research mathematician specialising in algebra and geometry. He was elected a Fellow of the Royal Society in 1908. His co-author Dr Alfred Young (1873-1940) was also a research mathematician before being ordained in 1908; in 1934 he too was elected a Fellow of the Royal Society. Abstract algebra was one of the new fields of study within mathematics which developed out of geometry during the nineteenth century. It became a major area of research in the late nineteenth and early twentieth centuries. First published in 1903, this book introduced the work on invariant theory of the German mathematicians Alfred Clebsch and Paul Gordan into British mathematics. It was considered the standard work on the subject.