The library suite JuliaStellarDynamics calculates stellar dynamics, including orbital transformations, basis expansions, finite Hilbert transforms, and linear response. The OrbitalElements.jl library transforms orbital coordinates in arbitrary central potentials and computes actions, frequencies, and resonance coordinates. AstroBasis.jl constructs and evaluates biorthogonal potential–density bases for spherical and disc systems, with support for user-defined bases. The library FiniteHilbertTransform.jl implements the finite Hilbert transform following Landau’s prescription using Legendre polynomials. Finally, LinearResponse.jl combines these tools to build response matrices and locate dynamical modes in the complex plane via Fourier-transformed basis elements, auxiliary functions, and the finite Hilbert transform. The JuliaStellarDynamics suite also offers interactive Colab notebooks that demonstrate key workflows without local installation.