Explore advanced mathematical concepts in this graduate-level lecture on singularities of vector fields and differential operators. Delve into topics such as the Susma Theorem, foliation by curves, reparameterization, and limit cycles. Learn about elementary German, normal forms, direct sum decomposition, and multivalued functions. Gain insights into the elegant definition of normal forms and the absence of resonant monomials in foliation. This comprehensive presentation by Daniel Cantergiani Panazzolo from Université de Haute Alsace is part of the Graduate Course on Transseries and Asymptotic Analysis at the Fields Institute.