This spring school focuses on some mathematical analysis’ methods for researching of the well-posedness and asymptotic behavior of solutions to evolution equations and dynamical systems. The main topics include spectral theory of functions, spectra of operators arising from dynamical systems, existence and smoothing properties of strongly continuous semigroups, well-posedness of evolution equations, interpolation functors and duality estimates. The abstract results are then applied to study the well-posedness and asymptotic behavior of dynamical systems and nonlocal boundary-valued problems as well as  solutions to Navier-Stokes equations and stability of fluid flows. This school is directed toward senior undergraduate students, graduate students, PhD students and young researchers. It creates also an environment for meeting and exchanging ideas and methods among mathematicians from Vietnam and abroad.