Interval analysis, roughly speaking, is concerned with interval-valued problems. We first motivate the reader and show that interval data naturally appear in many different fields. Then, we introduce the basic interval concepts, definitions, and notation; intervals, interval vectors, and interval matrices are the key objects that accompany the reader throughout the book. As a first step, we define the basic operations on intervals (interval arithmetic) and discuss their properties. Evaluation of general functions on intervals is a more challenging problem; we present only basic enclosure techniques here.