The text contains ten chapters, each originating either from a proper research paper or from an expository article describing a new approach to look at a thing well established or maybe containing a few new results. The reader will enjoy this mix of different flavours. The final chapter, "On A Multistage Randomized Statistical Test Structure" was the author's formal Bachelor's thesis and is the most extensive of all. The monograph thus, goes by the same title. In that paper, an effort has been made to show the strength of rejection of a parametric hypothesis explicitly by partitioning the acceptance and critical region into mutually exclusive and exhaustive subregions with appropriate probabilities assigned. As a consequence, we note that apart from appreciating the logically superior test structure, one can achieve much flexibility in the sense of reducing the probability of type - I error or increasing the power considerably depending on the partitions and the probabilities. Section A introduces the idea along with the formal definitions, calculations, advantages, numerical examples etc. Section B concerns the more mathematical side, focusing on a special case.