Textbook in PDF format This book introduces classical modal optics and discrete quantum systems using a common mathematical approach based on linear vector spaces. It explores the three key elements of photonic quantum information: the optical bimode, the qubit, and the photon. Both the bimode and qubit are represented as vectors in a two-dimensional linear vector space, but the qubit distinguishes itself through unique properties linked to quantum measurement. While optical bimodes can be mutually coupled, qubits can be entangled, enabling revolutionary quantum information technologies