Research Paper (postgraduate) from the year 2020 in the subject Mathematics - Analysis, grade: 9.5, , language: English, abstract: In present book the concepts of arithmetic progressions and its related sub-topics have been extended keeping in view the vital role of arithmetic sequences and series in many research areas. The extension of the arithmetic progression has been named as Multi-dimensional Arithmetic Progression with Multiplicity. In first chapter some results and properties have been discussed for traditional arithmetic progression, which will be known as one dimensional arithmetic progression with multiplicity one. In chapter two and three two dimensional arithmetic progressions with multiplicities one and two have been explained. In chapter four to six three dimensional arithmetic progressions with multiplicities one to three have been discussed. In chapter seven rth dimensional arithmetic progression with multiplicity one has been discussed, which can be considered as the superset of all arithmetic progressions having any number of common differences with multiplicity one. In chapter eight some scope of further extension has been discussed for new scholars. The book ends with the references from where some help have been taken in preparing the book including my published research papers.