Gravity.jl: Fast and accurate gravitational lens modeling in Julia

We present Gravity.jl , a new proprietary software for the modeling of gravitational lens systems. Gravity.jl is written in the Julia programming language, and is designed to be fast, accurate, and flexible. It can be used to model gravitational lens systems composed of multiple lensing planes, and to perform Bayesian inference on the lens model parameters. In this paper we present the theoretical and statistical ideas behind the code, and we describe its main features. In this first paper of the series, we focus on the modeling of point-like and small extended sources, for which we can linearize the lens equation. We show a practical use of Gravity.jl on a galaxy-scale lens, and we compare the results with those obtained with other codes. We also show how Gravity.jl can be used to perform Bayesian inference on cosmological parameters.