  In this Tutorial, we give a pedagogical introduction to Majorana bound states
(MBSs) arising in semiconducting nanostructures. We start by briefly reviewing
the well-known Kitaev chain toy model in order to introduce some of the basic
properties of MBSs before proceeding to describe more experimentally relevant
platforms. Here, our focus lies on simple `minimal' models where the Majorana
wave functions can be obtained explicitly by standard methods. In a first part,
we review the paradigmatic model of a Rashba nanowire with strong spin-orbit
interaction (SOI) placed in a magnetic field and proximitized by a conventional
$s$-wave superconductor. We identify the topological phase transition
separating the trivial phase from the topological phase and demonstrate how the
explicit Majorana wave functions can be obtained in the limit of strong SOI. In
a second part, we discuss MBSs engineered from proximitized edge states of
two-dimensional (2D) topological insulators. We introduce the Jackiw-Rebbi
mechanism leading to the emergence of bound states at mass domain walls and
show how this mechanism can be exploited to construct MBSs. Due to their recent
interest, we also include a discussion of Majorana corner states in 2D
second-order topological superconductors. This Tutorial is mainly aimed at
graduate students -- both theorists and experimentalists -- seeking to
familiarize themselves with some of the basic concepts in the field.
