Research Paper (postgraduate) from the year 2020 in the subject Mathematics - Analysis, grade: 9.6, , language: English, abstract: In present book the concepts of geometric progressions and its related sub-topics have been extended keeping in view the vital role of geometric progressions and series in many research areas. The extension of the geometric progression has been named as Multi-dimensional geometric Progression with Multiplicity. In first chapter some results and properties have been discussed for traditional geometric progression, which can be called one dimensional geometric progression with multiplicity one. In chapter two and three two dimensional geometric progressions with multiplicities one and two have been explained. In chapter four to six three dimensional geometric progressions with multiplicities one to three have been discussed. In chapter seven R-dimensional geometric progressions with multiplicity one has been discussed, which can be considered as the superset of all geometric progressions having any number of common ratios with multiplicity one. In chapter eight some scope of further extension has been discussed for new scholars and researchers. The book ends with the references from where some help have been taken in preparing the book including my published research papers and research book on multi-dimensional arithmetic progressions.