  The quantum mechanics formalism introduced new revolutionary concepts
challenging our everyday perceptions. Arguably, quantum entanglement, which
explains correlations that cannot be reproduced classically, is the most
notable of them. Besides its fundamental aspect, entanglement is also a
resource, fueling emergent technologies such as quantum simulators and
computers. The purpose of this chapter is to give a pedagogical introduction to
the topic with a special emphasis on the multipartite scenario, i.e.,
entanglement distributed among many degrees of freedom. Due to the
combinatorial complexity of this setting, particles can interact and become
entangled in a plethora of ways, which we characterize here. We start by
providing the necessary mathematical tools and elementary concepts from
entanglement theory. A part of this chapter will be devoted to classifying and
ordering entangled states. Then, we focus on various entanglement structures
useful in condensed-matter theory such as tensor-network states or symmetric
states useful for quantum-enhanced sensing. Finally, we discuss
state-of-the-art methods to detect and certify such correlations in
experiments, with some relevant illustrative examples.
