A Note on Metric-affine Gravity

The main purpose of this work is to give an overview of a gravity theory which has attracted a lot of physicists’ attention in the last decades, namely metric-affine gravity. We analyse a well-known expression in the literature for the Lie derivative of the metric in the case of metric-affine approach and discuss its consequences. There is also a historical analysis of this theory, which includes its most important findings. One comes to the conclusion with some viewpoints on the calculation of topological observables in that theory, which is viewed as topological gravity theory.