In this note, we introduce the new tool reSolve, a Monte Carlo differential cross-section and parton-level event generator whose main purpose is to add transverse momentum resummation to a general class of inclusive processes at hadron colliders, namely all those which do not involve hadrons or jets in the measured final state. This documentation refers to the first main version release, which will form the basis for continued developments, consequently it only implements the key features of those we plan to ultimately include. This article acts as a manual for the program; describing in detail its use, structure, validation and results; whilst also highlighting key aspects of the resummation formalism applied. It details the two classes of processes so far included; these are diphoton production and Drell–Yan production. A main concept behind the development of the tool is that it is a hands-on white box for the user: significant effort has been made to give the program a modular structure, making the various parts which comprise it independent of each other as much as possible and ensuring they are transparently documented, customisable and, in principle, replaceable with something that may better serve the user's needs. reSolve is a new C++ program, based on an evolution of the private Fortran code 2gres, it is also influenced by the DYRes Fortran code. This initial version calculates the low transverse momentum contribution to the fully differential cross-section for two main categories of processes; the inclusive production of two photons, and inclusive Drell–Yan production. In all cases resummation up to Next-to-Next-to-Leading Logarithm (NNLL) is included. We aim to extend the program to several more processes in the near future. The program is publicly available on Github. Program summary: Program title: reSolve Program Files doi: http://dx.doi.org/10.17632/4djmkmy69c.1 Licensing provisions: GNU General Public License 3 Programming language: C++, fortran External routines: minuit and Cuba Nature of problem: Calculating the transverse momentum spectrum, including resummation, for a general process at hadron colliders. Solution method: Monte Carlo generation of the phase space points and phase space integration to allow the production of differential distributions, each phase space point itself has to be inverse Fourier transformed and double inverse Mellin transformed to allow the resummation, following the usual transverse momentum resummation impact parameter space formalism. reSolve performs up to Next-to-Next-to-Leading Logarithm resummation (NNLL). Restrictions: So far only diphoton production in the Standard Model (background, not including Higgs) and Drell–Yan production are included, nonetheless the program is designed to allow further extensions to additional processes, including by the user. The limitations on the processes possible to implement are that they must be hadron–hadron collisions producing a non-strongly interacting measured final state system. This first main implementation of reSolve calculates only the resummed part of the differential cross-section, which is dominant at low transverse momentum, this has to be matched with the usual finite contributions to obtain the spectrum over the whole transverse momentum range.