Dispersion forces acting on both atoms and bodies play a key role in modern nanotechnology. This book provides an accessible introduction to this intriguing subject. Macroscopic quantum electrodynamics in linear, causal media is introduced as a powerful method for understanding and quantifying dispersion forces in a vast range of realistic scenarios. In contrast to the normal-mode quantum electrodynamics traditionally used to study dispersion forces, the new approach allows to consider realistic material properties including absorption and is flexible enough to be applied to a broad range of geometries. The basic physical concepts and theoretical steps lead to the derivation of outlined general expressions for ground-state Casimir, Casimir-Polder and van der Waals forces. As illustrated by a number of examples, these expressions can easily be used to study forces between objects of various shapes and materials, including effects like material absorption, nontrivial magnetic properties and varying object thickness and curvature. More advanced aspects are discussed in Vol. II. The book includes an inspirational foreword by I.H. Brevik.