Over the last five decades, the development of logic enriches the fields of science and engineering, particularly computer science and information technology. Also the algebraic concepts are being continuously updated in the research structure of many universities around the world. With this purpose in necessity has also come a rise in the need for researching within these spaces and very detailed literature exists on how to best utilize this classical and emerging area for researching activities. This book, therefore, provides a new metric of success for readers to some of the abstract thinking that provides modern abstract algebra and a transition from elementary research topics to advanced topics in lattice theory. This book will also help the students and researchers of various universities to build strong foundation in applied abstract algebra. The main aim of this book is to study the structure of annihilator ideals, annulets and ?-ideals in almost distributive lattices. Characterizations of some algebraic structures like normal ADLs, generaliged Stone ADLs, weakly disjunctive ADLs e.t.c can also be observed in this book.