  The aim of this Tutorial is to give a pedagogical introduction into
realizations of Majorana fermions, usually termed as Majorana bound states
(MBS), in condensed matter systems with magnetic textures. We begin by
considering the Kitaev chain model of 'spinless' fermions and show how two
'half' fermions can appear at chain ends due to interactions. By considering
this model and its two-dimensional generalization, we emphasize intricate
relation between topological superconductivity and possible realizations of
MBS. We further discuss how 'spinless' fermions can be realized in more
physical systems, e.g., by employing the spin-momentum locking. Next, we
demonstrate how magnetic textures can be used to induce synthetic or fictitious
spin-orbit interactions, and, thus, stabilize MBS. We describe a general
approach that works for arbitrary textures and apply it to skyrmions. We show
how MBS can be stabilized by elongated skyrmions, certain higher order
skyrmions, and chains of skyrmions. We also discuss how braiding operations can
be performed with MBS stabilized on magnetic skyrmions. This Tutorial is aimed
at students at graduate level.
