The present work proposes a detailed presentation of the main types of non-parametric statistical tests, the conditions and ways in which they can be applied in the study of different categories of problems. It has as its starting point the volume  from 2010, a material that illustrates different techniques for verifying statistical hypotheses with the help of two general-purpose mathematical software, Mathematica and Maple. The topics addressed generally follow those of  (tests for proportions, rank-based tests, concordance tests), extending and completing them with a rigorous mathematical foundation. New topics were also added, motivated by the emergence and integration into common practice of some modern, computationally intensive techniques (bootstrap methods, permutation techniques).
In this paper we will use the R language to exemplify the presented methods, a decision motivated by the wide range of facilities it provides. The development of new statistical methods and algorithms is quickly reflected in the offer made available to those interested in the form of R packages that can be easily downloaded and used. The reading of this text starts from the premise that, along with introductory level statistics knowledge, the reader has basic knowledge of using R (working with vectors, dataframes, factors, minimal programming skills), in this sense there is a variety of courses, tutorials and resources available to users online and for free. The paper includes the complete code for each of the examples presented.
We hope that this volume can be a useful reference for researchers in applied fields who need to use non-parametric techniques to verify statistical hypotheses, but also for students from mathematics and computer science majors.