  This article is a pedagogical introduction to relativistic quantum mechanics
of the free Majorana particle. This relatively simple theory differs from the
well-known quantum mechanics of the Dirac particle in several important
aspects. We present its three equivalent formulations. Next, so called axial
momentum observable is introduced, and general solution of the Dirac equation
is discussed in terms of eigenfunctions of that operator. Pertinent irreducible
representations of the Poincar\'e group are discussed. Finally, we show that in
the case of massless Majorana particle the quantum mechanics can be
reformulated as a spinorial gauge theory.
