This book is our attempt to answer the question, "Is it possible to decompose any graph G with n vertices, lacking any specific symmetry of the underlying structures?" This book presents a solution to this question by developing iterative techniques in an intuitive, simple, and visual way without losing the essence of the underlying mathematics. We trust that this method of decomposing any graph into known subgraphs will open new directions in graph decomposition. This book will be of interest to researchers in graph theory and discrete mathematics.