  Majorana bound states are quasiparticle excitations localized at the
boundaries of a topologically nontrivial superconductor. They are zero-energy,
charge-neutral, particle-hole symmetric, and spatially-separated end modes
which are topologically protected by the particle-hole symmetry of the
superconducting state. Due to their topological nature, they are robust against
local perturbations and, in an ideal environment, free from decoherence.
Furthermore, unlike ordinary fermions and bosons, the adiabatic exchange of
Majorana modes is noncommutative, i.e., the outcome of exchanging two or more
Majorana modes depends on the order in which exchanges are performed. These
properties make them ideal candidates for the realization of topological
quantum computers. In this tutorial, I will present a pedagogical review of 1D
topological superconductors and Majorana modes in quantum nanowires. I will
give an overview of the Kitaev model and the more realistic Oreg-Lutchyn model,
discuss the experimental signatures of Majorana modes, and highlight their
relevance in the field of topological quantum computation. This tutorial may
serve as a pedagogical and relatively self-contained introduction for graduate
students and researchers new to the field, as well as an overview of the
current state-of-the-art of the field and a reference guide to specialists.
