The direct-summation of N gravitational forces is a complex problem for which there is not analytical solution.Dense stellar systems such as galactic nuclei and stellar clusters are the loci of different interesting problems.In this work we present a new GPU,direct-summation N-body integrator written from scratch and based on the Hermite scheme.The first release of the code consists of the Hermite integrator for a system of N bodies with softening.We run satisfactory a series of well-established tests:Cumulative and relative energy error as a function of different parameters like η,time and the amount of particles.Performance of our implementations(GPU,MPI,OpenMP)Wall-clock elapsed time as a function of N,η Lagrange radii,and the mass-density and radius of the core.We find an acceleration factor of about 90 of the GPU version in a single node as compared to the Serial-Single-CPU one.We additionally investigate the impact of using softening in the dynamics of a dense cluster.We study how it affects the two body relaxation,as compared with another code,NBODY6,which uses KS regularisation,so as to understand the role of softening in the evolution of the system.This initial work is the introduction to a series of papers,currently in development,that will present more and more realistic scenarios,starting for a proper treatment for binary evolution,close encounters and the role of a massive black hole.