  This work reports on the development and numerical implementation of the
linear electromagnetic gyrokinetic (GK) model in a tokamak flux-tube geometry
using a moment approach based on the expansion of the perturbed distribution
function on a velocity-space Hermite-Laguerre polynomials basis. A hierarchy of
equations of the expansion coefficients, referred to as the gyro-moments (GM),
is derived. We verify the numerical implementation of the GM hierarchy in the
collisionless limit by performing a comparison with the continuum GK code GENE,
recovering the linear properties of the ion-temperature gradient, trapped
electron, kinetic ballooning, and microtearing modes, as well as the
collisionless damping of zonal flows. The present investigation reveals the
ability of the GM approach to describe fine velocity-space scale structures
appearing near the trapped and passing boundary and kinetic effects associated
with parallel and perpendicular particle drifts. In addition, the effects of
collisions are studied using advanced collision operators, including the GK
Coulomb collision operator. The main findings are that the number of GMs
necessary for convergence decreases with plasma collisionality and is lower for
pressure gradient-driven modes, such as in H-mode pedestal regions, compared to
instabilities driven by trapped particles and magnetic gradient drifts often
found in the core. The accuracy of approximations often used to model
collisions (relative to the GK Coulomb operator) is studied, showing
differences between collision operator models that increase with collisionality
and electron temperature gradient in the case of TEM. The present linear
analysis demonstrates that the GM approach efficiently describes the plasma
dynamics for typical parameters of the tokamak boundary, ranging from the
low-collisionality banana H-mode to the high-collisionality Pfirsch-Schl\"uter
conditions.
