This thesis investigates multifractality as a tool to analyse the spatial patterns emerging from urban inequality. In our context, inequality is defined as a difference between individuals in economic welfare (in the tradition of Dalton and Sen). As such, it considers the typical household income distribution, but also variables such as real estate and energy consumption. These variables can be transformed into mathematical measures which present diverse extent of self-similarities explained by the self-organisation processes resulting from an intense competition for space. The multifractal methodology can exploit these self-similarities to produce precise local statistical information even when the usual tools fail due to an excessive complexity. The analysis is performed on large geographical datasets for London, Paris, New-York and Kyoto. The main results are a decrease in multifractality with modernisation that can be understood as an arguably positive homogenisation, but also a negative loss of diversity; striking similarities in the independent evolution of the spatial repartition of land and housing prices across the globe during the 20th century; and discrepancies between income and the other measures, in accordance with the idea that income alone is not enough to fully characterize inequality. The most important result, however, is the validation after comparison with the traditional inequality and segregation measures that multifractality is a high-performing spatial inequality indicator. It is in particular able to extend the exposure and clustering dimensions of segregation to ordinal continuous variables
