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We give a basic introduction to Unimodular Gravity both at the classical and quantum level, discussing the role it might play in the interpretation of the Cosmological Constant problem. The aim of this work is at the basic level but techniques used at the research level are presented. The goal of the paper is to enable the reader to grasp the interest of UG while making the recent literature on the topic accessible.

We have studied a lagrangian in which the Einstein-Hilbert term is deformed by the Weyl cube operator, which is the lowest-dimension operator that is non-vanishing on shell and appears as a two-loop counterterm. There is a tension between the Schwarzschild de Sitter (SdS) spacetime and this operator, which we study in some detail.

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