Klein's lectures, published posthumously in two volumes (1926–1927), offer an "advanced standpoint" on how the century's great minds unified disparate branches of mathematics. Key Themes in 19th-Century Mathematics

Klein highlighted the brilliant achievements of Riemann and Weierstrass in function theory. He saw the 19th century as a period where transcendental methods (like Riemann surfaces) and algebraic methods (like invariant theory) began to merge.