Euler published "Mechanica sive motus scientia analytice exposita", a groundbreaking work that applied analytical methods to the study of mechanics. It laid the foundation for classical mechanics.

Euler's "Introductio in analysin infinitorum" revolutionized the study of analysis by establishing concepts of functions and systematizing calculus.

Euler's work on differential calculus. A major milestone in calculus and differential equations.

Euler published "Institutiones calculi integralis", an work regarding the integral calculus, the counterpart to his work on differential calculus.

Euler's textbook on algebra, "Vollständige Anleitung zur Algebra", became a standard work on the subject and helped to popularize algebraic concepts.

Euler made significant contributions to number theory, including the development of Euler's totient function, Fermat's Last Theorem for n=3 and n=4, and the law of quadratic reciprocity.

Euler's contributions to fluid dynamics include Euler equations.