To effectively manage Technical Debt (TD), we need reliable means to quantify it. We conducted a Systematic Mapping Study (SMS) where we identified 39 quantification approaches for Code, Design, and Architecture TD. We analyzed concepts and metrics discussed in these quantification approaches by classifying the quantification approaches based on a set of abstract TD Quantification (TDQ) concepts and their high-level themes, process/time, cost, benefit, probability, and priority, which we developed during our SMS. This helped identify gaps in the literature and to propose future research directions. Among the abstract TDQ concepts discussed in the different quantification approaches, TD item, TD remediation cost, TD interest, and Benefit of remediating TD were the most frequently discussed concepts. They were also supported by some form of measurement. However, some TDQ concepts were poorly examined, for example, the benefit of taking TD. It was evident that cost concepts were more frequently quantified among the approaches, while benefit concepts were not. Most of the approaches focused on remediating TD in retrospect rather than quantifying TD to strategically use it during software development. This raises the question of whether existing approaches reliably quantify TD and suggests the need to further explore TD quantification.