"Daprima importa sappere di che cosa si tratta." ("The ?rst thing is to know what the talk is about".) Attributed to Vilfredo Pareto. This book results from my continuous and deep interest in multiple criteria decision making (MCDM). Eleven years ago I wrote in my p- vious monograph: "This work results from my interest in the ?eld of vector optimization. I stumbled ?rst upon this subject in 1982 [ ... ]. I was attracted then by a gap between vector optimization used to serve as a formal model for multiple objective decision problems and the - cision problems themselves, the gap nonexistent in scalar optimization. Roughly speaking, vector optimization provides methods for ranking - cisions according to a partial order whereas decision making requires a linear ordering of decisions." This declaration is still valid and nothing needs to be changed. To be more speci?c, this book is a fruit of my dissatisfaction with the current state-of-the-art of MCDM. MCDM is a branch of science, whose declared ultimate goal is to provide practical tools. However, we cannot say, and this is regrettable, that all present MCDM methods and algorithms are in popular use by those who make complex decisions and for that purpose are in need of methodological or computational support.