The document 'Foundations of Narrative Bibliometrics' provides an analysis of the evolution of scientific assessment, highlighting the influence of manifestos such as DORA and CoARA in shaping ethical and responsible practices in academia, as well as their assimilation by Spanish scientific policies. It connects this context with the contributions of evaluative bibliometrics, emphasising the transition towards a more integrative approach that advocates for a balance between quantitative and qualitative methods in research evaluation. Furthermore, it underscores how the Narrative Curriculum has emerged as one of the fundamental tools in new evaluation processes, as it allows for the description of the complexity and context of academic achievements. Narrative Bibliometrics is proposed, defined as the use of bibliometric indicators to generate narratives and stories that support the defence and exposition of a scientific curriculum and/or its individual contributions within the framework of a scientific evaluation process. To introduce the reader, it presents, in a non exhaustive manner, sources, indicators, and practical cases for effectively applying narrative bibliometrics in various scientific evaluation contexts. Hence, this document is offered as an introductory tool for evaluators and researchers for a responsible use of bibliometric indicators.